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1707.01891 | 4 | âAlso at the Department of Computing Science, University of Alberta, [email protected] 1An implementation of Trust-PCL is available at https://github.com/tensorflow/models/ tree/master/research/pcl_rl
1
Published as a conference paper at ICLR 2018
optimal policy and value function satisfy a set of pathwise consistency properties along any sam- pled path (Nachum et al., 2017), which allows both on and off-policy data to be incorporated in an actor-critic algorithm, PCL. The original PCL algorithm optimized an entropy regularized max- imum reward objective and was evaluated on relatively simple tasks. Here we extend the ideas of PCL to achieve strong results on standard, challenging continuous control benchmarks. The main observation is that by alternatively augmenting the maximum reward objective with a relative en- tropy regularizer, the optimal policy and values still satisfy a certain set of pathwise consistencies along any sampled trajectory. The resulting objective is equivalent to maximizing expected reward subject to a penalty-based constraint on divergence from a reference (i.e., previous) policy. | 1707.01891#4 | Trust-PCL: An Off-Policy Trust Region Method for Continuous Control | Trust region methods, such as TRPO, are often used to stabilize policy
optimization algorithms in reinforcement learning (RL). While current trust
region strategies are effective for continuous control, they typically require
a prohibitively large amount of on-policy interaction with the environment. To
address this problem, we propose an off-policy trust region method, Trust-PCL.
The algorithm is the result of observing that the optimal policy and state
values of a maximum reward objective with a relative-entropy regularizer
satisfy a set of multi-step pathwise consistencies along any path. Thus,
Trust-PCL is able to maintain optimization stability while exploiting
off-policy data to improve sample efficiency. When evaluated on a number of
continuous control tasks, Trust-PCL improves the solution quality and sample
efficiency of TRPO. | http://arxiv.org/pdf/1707.01891 | Ofir Nachum, Mohammad Norouzi, Kelvin Xu, Dale Schuurmans | cs.AI | ICLR 2018 | null | cs.AI | 20170706 | 20180222 | [
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1707.01891 | 5 | We exploit this observation to propose a new off-policy trust region algorithm, Trust-PCL, that is able to exploit off-policy data to train policy and value estimates. Moreover, we present a simple method for determining the coefï¬cient on the relative entropy regularizer to remain agnostic to reward scale, hence ameliorating the task of hyperparameter tuning. We ï¬nd that the incorporation of a relative entropy regularizer is crucial for good and stable performance. We evaluate Trust- PCL against TRPO, and observe that Trust-PCL is able to solve difï¬cult continuous control tasks, while improving the performance of TRPO both in terms of the ï¬nal reward achieved as well as sample-efï¬ciency.
# 2 RELATED WORK
Trust Region Methods. Gradient descent is the predominant optimization method for neural networks. A gradient descent step is equivalent to solving a trust region constrained optimization,
minimize â¬(0 + d0) = â¬(0) + Ve(0)'dd st. dOâ¢dO<e, (1)
dOâ¢dO<e,
which yields the locally optimal update dd = ânV¢(0) such that 7 = v/e/||V(4)||; hence by considering a Euclidean ball, gradient descent assumes the parameters lie in a Euclidean space. | 1707.01891#5 | Trust-PCL: An Off-Policy Trust Region Method for Continuous Control | Trust region methods, such as TRPO, are often used to stabilize policy
optimization algorithms in reinforcement learning (RL). While current trust
region strategies are effective for continuous control, they typically require
a prohibitively large amount of on-policy interaction with the environment. To
address this problem, we propose an off-policy trust region method, Trust-PCL.
The algorithm is the result of observing that the optimal policy and state
values of a maximum reward objective with a relative-entropy regularizer
satisfy a set of multi-step pathwise consistencies along any path. Thus,
Trust-PCL is able to maintain optimization stability while exploiting
off-policy data to improve sample efficiency. When evaluated on a number of
continuous control tasks, Trust-PCL improves the solution quality and sample
efficiency of TRPO. | http://arxiv.org/pdf/1707.01891 | Ofir Nachum, Mohammad Norouzi, Kelvin Xu, Dale Schuurmans | cs.AI | ICLR 2018 | null | cs.AI | 20170706 | 20180222 | [
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1707.01891 | 6 | However, in machine learning, particularly in the context of multi-layer neural network training, Euclidean geometry is not necessarily the best way to characterize proximity in parameter space. It is often more effective to define an appropriate Riemannian metric that respects the loss surface (Amari (2012), which allows much steeper descent directions to be identified within a local neigh- borhood (e.g., [Amari] (1998); [Martens & Grosse] (2015p). Whenever the loss is defined in terms of a Bregman divergence between an (unknown) optimal parameter 6* and model parameter 0, i.e, (0) = Dr(6*, 8), it is natural to use the same divergence to form the trust region:
minimize Dp(6*,9+d0) s.t. Dp(0,0+d0) <e. (2) | 1707.01891#6 | Trust-PCL: An Off-Policy Trust Region Method for Continuous Control | Trust region methods, such as TRPO, are often used to stabilize policy
optimization algorithms in reinforcement learning (RL). While current trust
region strategies are effective for continuous control, they typically require
a prohibitively large amount of on-policy interaction with the environment. To
address this problem, we propose an off-policy trust region method, Trust-PCL.
The algorithm is the result of observing that the optimal policy and state
values of a maximum reward objective with a relative-entropy regularizer
satisfy a set of multi-step pathwise consistencies along any path. Thus,
Trust-PCL is able to maintain optimization stability while exploiting
off-policy data to improve sample efficiency. When evaluated on a number of
continuous control tasks, Trust-PCL improves the solution quality and sample
efficiency of TRPO. | http://arxiv.org/pdf/1707.01891 | Ofir Nachum, Mohammad Norouzi, Kelvin Xu, Dale Schuurmans | cs.AI | ICLR 2018 | null | cs.AI | 20170706 | 20180222 | [
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1707.01891 | 7 | minimize Dp(6*,9+d0) s.t. Dp(0,0+d0) <e. (2)
The natural gradient (Amari|/1998) is a generalization of gradient descent where the Fisher informa- tion matrix F'(9) is used ti to define the local geometry of the parameter space around @. If a parameter update is constrained by d@" F(6)d@ < ¢, a descent direction of d@ = ânF(0)~!V£(6) is obtained. This geometry is especially effective for optimizing the log-likelihood of a conditional probabilistic model, where the objective is in fact the KL divergence Dx 1,(9", #). The local optimization is,
minimize Dx, (6",9+d0) s.t. Dxi(0,0+d0) = <e. (3)
# ue | 1707.01891#7 | Trust-PCL: An Off-Policy Trust Region Method for Continuous Control | Trust region methods, such as TRPO, are often used to stabilize policy
optimization algorithms in reinforcement learning (RL). While current trust
region strategies are effective for continuous control, they typically require
a prohibitively large amount of on-policy interaction with the environment. To
address this problem, we propose an off-policy trust region method, Trust-PCL.
The algorithm is the result of observing that the optimal policy and state
values of a maximum reward objective with a relative-entropy regularizer
satisfy a set of multi-step pathwise consistencies along any path. Thus,
Trust-PCL is able to maintain optimization stability while exploiting
off-policy data to improve sample efficiency. When evaluated on a number of
continuous control tasks, Trust-PCL improves the solution quality and sample
efficiency of TRPO. | http://arxiv.org/pdf/1707.01891 | Ofir Nachum, Mohammad Norouzi, Kelvin Xu, Dale Schuurmans | cs.AI | ICLR 2018 | null | cs.AI | 20170706 | 20180222 | [
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1707.01891 | 8 | minimize Dx, (6",9+d0) s.t. Dxi(0,0+d0) = <e. (3)
# ue
ames natural gradient approximates the trust region by D(a, b) © (a â a)(a â b), which s accurate up to a second order Taylor approximation. Previous work (Kakade| Kaba 005) Bore Schneider 2003 } Peters & Schaal|/2008 } Schulman et al. 2015) has applied natural gradient to policy optimization, locally improving expected reward subject to variants of do'F F(0)d0 < e. Recently, TRPO (Schulman et al. 2015} 2016) has achieved state-of-the-art results in continuous control by adding several approximations to the natural gradient to make nonlinear policy optimization feasible.
Another approach to trust region optimization is given by proximal gradient methods (Parikh et al., 2014). The class of proximal gradient methods most similar to our work are those that replace the hard constraint in (2) with a penalty added to the objective. These techniques have recently become popular in RL (Wang et al., 2016; Heess et al., 2017; Schulman et al., 2017b), although in terms of ï¬nal reward performance on continuous control benchmarks, TRPO is still considered to be the state-of-the-art.
2 | 1707.01891#8 | Trust-PCL: An Off-Policy Trust Region Method for Continuous Control | Trust region methods, such as TRPO, are often used to stabilize policy
optimization algorithms in reinforcement learning (RL). While current trust
region strategies are effective for continuous control, they typically require
a prohibitively large amount of on-policy interaction with the environment. To
address this problem, we propose an off-policy trust region method, Trust-PCL.
The algorithm is the result of observing that the optimal policy and state
values of a maximum reward objective with a relative-entropy regularizer
satisfy a set of multi-step pathwise consistencies along any path. Thus,
Trust-PCL is able to maintain optimization stability while exploiting
off-policy data to improve sample efficiency. When evaluated on a number of
continuous control tasks, Trust-PCL improves the solution quality and sample
efficiency of TRPO. | http://arxiv.org/pdf/1707.01891 | Ofir Nachum, Mohammad Norouzi, Kelvin Xu, Dale Schuurmans | cs.AI | ICLR 2018 | null | cs.AI | 20170706 | 20180222 | [
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1707.01891 | 9 | 2
Published as a conference paper at ICLR 2018
Norouzi et al. (2016) make the observation that entropy regularized expected reward may be ex- pressed as a reversed KL divergence DKL(θ, θâ), which suggests that an alternative to the constraint in (3) should be used when such regularization is present:
s.t. Dr (0+, 0) = do" F(6 + d0)d0 <e.
minimize DKL(θ + dθ, θâ)
(4)
Unfortunately, this update requires computing the Fisher matrix at the endpoint of the update. The use of F'(@) in previous work can be considered to be an approximation when entropy regularization is present, but it is not ideal, particularly if dé is large. In this paper, by contrast, we demonstrate that the optimal dé under the reverse KL constraint Dx,,(@ + dé, 0) < ⬠can indeed be characterized. Defining the constraint in this way appears to be more natural and effective than that of TRPO. | 1707.01891#9 | Trust-PCL: An Off-Policy Trust Region Method for Continuous Control | Trust region methods, such as TRPO, are often used to stabilize policy
optimization algorithms in reinforcement learning (RL). While current trust
region strategies are effective for continuous control, they typically require
a prohibitively large amount of on-policy interaction with the environment. To
address this problem, we propose an off-policy trust region method, Trust-PCL.
The algorithm is the result of observing that the optimal policy and state
values of a maximum reward objective with a relative-entropy regularizer
satisfy a set of multi-step pathwise consistencies along any path. Thus,
Trust-PCL is able to maintain optimization stability while exploiting
off-policy data to improve sample efficiency. When evaluated on a number of
continuous control tasks, Trust-PCL improves the solution quality and sample
efficiency of TRPO. | http://arxiv.org/pdf/1707.01891 | Ofir Nachum, Mohammad Norouzi, Kelvin Xu, Dale Schuurmans | cs.AI | ICLR 2018 | null | cs.AI | 20170706 | 20180222 | [
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1707.01891 | 10 | Softmax Consistency. To comply with the information geometry over policy parameters, previous work has used the relative entropy (i.e., KL divergence) to regularize policy optimization; resulting in a softmax relationship between the optimal policy and state values (Peters et al., 2010; Azar et al., 2012; 2011; Fox et al., 2016; Rawlik et al., 2013) under single-step rollouts. Our work is unique in that we leverage consistencies over multi-step rollouts.
The existence of multi-step softmax consistencies has been noted by prior workâï¬rst by Nachum et al. (2017) in the presence of entropy regularization. The existence of the same consistencies with relative entropy has been noted by Schulman et al. (2017a). Our work presents multi-step con- sistency relations for a hybrid relative entropy plus entropy regularized expected reward objective, interpreting relative entropy regularization as a trust region constraint. This work is also distinct from prior work in that the coefï¬cient of relative entropy can be automatically determined, which we have found to be especially crucial in cases where the reward distribution changes dramatically during training. | 1707.01891#10 | Trust-PCL: An Off-Policy Trust Region Method for Continuous Control | Trust region methods, such as TRPO, are often used to stabilize policy
optimization algorithms in reinforcement learning (RL). While current trust
region strategies are effective for continuous control, they typically require
a prohibitively large amount of on-policy interaction with the environment. To
address this problem, we propose an off-policy trust region method, Trust-PCL.
The algorithm is the result of observing that the optimal policy and state
values of a maximum reward objective with a relative-entropy regularizer
satisfy a set of multi-step pathwise consistencies along any path. Thus,
Trust-PCL is able to maintain optimization stability while exploiting
off-policy data to improve sample efficiency. When evaluated on a number of
continuous control tasks, Trust-PCL improves the solution quality and sample
efficiency of TRPO. | http://arxiv.org/pdf/1707.01891 | Ofir Nachum, Mohammad Norouzi, Kelvin Xu, Dale Schuurmans | cs.AI | ICLR 2018 | null | cs.AI | 20170706 | 20180222 | [
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1707.01891 | 11 | Most previous work on softmax consistency (e.g., Fox et al. (2016); Azar et al. (2012); Nachum et al. (2017)) have only been evaluated on relatively simple tasks, including grid-world and discrete algo- rithmic environments. Rawlik et al. (2013) conducted evaluations on simple variants of the CartPole and Pendulum continuous control tasks. More recently, Haarnoja et al. (2017) showed that soft Q- learning (a single-step special case of PCL) can succeed on more challenging environments, such as a variant of the Swimmer task we consider below. By contrast, this paper presents a successful appli- cation of the softmax consistency concept to difï¬cult and standard continuous-control benchmarks, resulting in performance that is competitive with and in some cases beats the state-of-the-art.
# 3 NOTATION & BACKGROUND | 1707.01891#11 | Trust-PCL: An Off-Policy Trust Region Method for Continuous Control | Trust region methods, such as TRPO, are often used to stabilize policy
optimization algorithms in reinforcement learning (RL). While current trust
region strategies are effective for continuous control, they typically require
a prohibitively large amount of on-policy interaction with the environment. To
address this problem, we propose an off-policy trust region method, Trust-PCL.
The algorithm is the result of observing that the optimal policy and state
values of a maximum reward objective with a relative-entropy regularizer
satisfy a set of multi-step pathwise consistencies along any path. Thus,
Trust-PCL is able to maintain optimization stability while exploiting
off-policy data to improve sample efficiency. When evaluated on a number of
continuous control tasks, Trust-PCL improves the solution quality and sample
efficiency of TRPO. | http://arxiv.org/pdf/1707.01891 | Ofir Nachum, Mohammad Norouzi, Kelvin Xu, Dale Schuurmans | cs.AI | ICLR 2018 | null | cs.AI | 20170706 | 20180222 | [
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1707.01891 | 12 | # 3 NOTATION & BACKGROUND
We model an agentâs behavior by a policy distribution Ï(a | s) over a set of actions (possibly discrete or continuous). At iteration t, the agent encounters a state st and performs an action at sampled from Ï(a | st). The environment then returns a scalar reward rt â¼ r(st, at) and transitions to the next state st+1 â¼ Ï(st, at). When formulating expectations over actions, rewards, and state transitions we will often omit the sampling distributions, Ï, r, and Ï, respectively.
Maximizing Expected Reward. The standard objective in RL is to maximize expected future discounted reward. We formulate this objective on a per-state basis recursively as
Orr (8,7) = Ears [r + YOpr(sâ,7)] - (5) The overall, state-agnostic objective is the expected per-state objective when states are sampled from interactions with the environment:
OER(Ï) = Es[OER(s, Ï)].
(6)
Most policy-based algorithms, critic (Konda & Tsitsiklis, 2000), aim to optimize OER given a parameterized policy. | 1707.01891#12 | Trust-PCL: An Off-Policy Trust Region Method for Continuous Control | Trust region methods, such as TRPO, are often used to stabilize policy
optimization algorithms in reinforcement learning (RL). While current trust
region strategies are effective for continuous control, they typically require
a prohibitively large amount of on-policy interaction with the environment. To
address this problem, we propose an off-policy trust region method, Trust-PCL.
The algorithm is the result of observing that the optimal policy and state
values of a maximum reward objective with a relative-entropy regularizer
satisfy a set of multi-step pathwise consistencies along any path. Thus,
Trust-PCL is able to maintain optimization stability while exploiting
off-policy data to improve sample efficiency. When evaluated on a number of
continuous control tasks, Trust-PCL improves the solution quality and sample
efficiency of TRPO. | http://arxiv.org/pdf/1707.01891 | Ofir Nachum, Mohammad Norouzi, Kelvin Xu, Dale Schuurmans | cs.AI | ICLR 2018 | null | cs.AI | 20170706 | 20180222 | [
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1707.01891 | 13 | (6)
Most policy-based algorithms, critic (Konda & Tsitsiklis, 2000), aim to optimize OER given a parameterized policy.
Path Consistency Learning (PCL). Inspired by Williams & Peng (1991), Nachum et al. (2017) augment the objective OER in (5) with a discounted entropy regularizer to derive an objective,
OENT(s, Ï) = OER(s, Ï) + Ï H(s, Ï) , where Ï â¥ 0 is a user-speciï¬ed temperature parameter that controls the degree of entropy regular- ization, and the discounted entropy H(s, Ï) is recursively deï¬ned as
H(s,7) = Ea,s[âlog (a | s) + yH(sâ, 7)] - (8)
3
(7)
Published as a conference paper at ICLR 2018
Note that the objective OENT(s, Ï) can then be re-expressed recursively as,
Ognt(s,7) = Eayr,sâ[r â T log r(a | s) + yOrnr(sâ, 7)] - (9) | 1707.01891#13 | Trust-PCL: An Off-Policy Trust Region Method for Continuous Control | Trust region methods, such as TRPO, are often used to stabilize policy
optimization algorithms in reinforcement learning (RL). While current trust
region strategies are effective for continuous control, they typically require
a prohibitively large amount of on-policy interaction with the environment. To
address this problem, we propose an off-policy trust region method, Trust-PCL.
The algorithm is the result of observing that the optimal policy and state
values of a maximum reward objective with a relative-entropy regularizer
satisfy a set of multi-step pathwise consistencies along any path. Thus,
Trust-PCL is able to maintain optimization stability while exploiting
off-policy data to improve sample efficiency. When evaluated on a number of
continuous control tasks, Trust-PCL improves the solution quality and sample
efficiency of TRPO. | http://arxiv.org/pdf/1707.01891 | Ofir Nachum, Mohammad Norouzi, Kelvin Xu, Dale Schuurmans | cs.AI | ICLR 2018 | null | cs.AI | 20170706 | 20180222 | [
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1707.01891 | 14 | Nachum et al. (2017) show that the optimal policy Ïâ for OENT and V â(s) = OENT(s, Ïâ) mutually satisfy a softmax temporal consistency constraint along any sequence of states s0, . . . , sd starting at s0 and a corresponding sequence of actions a0, . . . , adâ1:
d-1 V*(80) = E.|7"V"(sa) + 9 (ri ~ tT log" (ailsi)) | - (10) i=0
This observation led to the development of the PCL algorithm, which attempts to minimize squared error between the LHS and RHS of (10) to simultaneously optimize parameterized Ïθ and VÏ. Im- portantly, PCL is applicable to both on-policy and off-policy trajectories. | 1707.01891#14 | Trust-PCL: An Off-Policy Trust Region Method for Continuous Control | Trust region methods, such as TRPO, are often used to stabilize policy
optimization algorithms in reinforcement learning (RL). While current trust
region strategies are effective for continuous control, they typically require
a prohibitively large amount of on-policy interaction with the environment. To
address this problem, we propose an off-policy trust region method, Trust-PCL.
The algorithm is the result of observing that the optimal policy and state
values of a maximum reward objective with a relative-entropy regularizer
satisfy a set of multi-step pathwise consistencies along any path. Thus,
Trust-PCL is able to maintain optimization stability while exploiting
off-policy data to improve sample efficiency. When evaluated on a number of
continuous control tasks, Trust-PCL improves the solution quality and sample
efficiency of TRPO. | http://arxiv.org/pdf/1707.01891 | Ofir Nachum, Mohammad Norouzi, Kelvin Xu, Dale Schuurmans | cs.AI | ICLR 2018 | null | cs.AI | 20170706 | 20180222 | [
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1707.01891 | 15 | Trust Region Policy Optimization (TRPO). As noted, standard policy-based algorithms for max- imizing OER can be unstable and require small learning rates for training. To alleviate this issue, Schulman et al. (2015) proposed to perform an iterative trust region optimization to maximize OER. At each step, a prior policy ËÏ is used to sample a large batch of trajectories, then Ï is subsequently optimized to maximize OER while remaining within a constraint deï¬ned by the average per-state KL-divergence with ËÏ. That is, at each iteration TRPO solves the constrained optimization problem,
maximize Oge(t) 8.t. â Esnap[ KL (#(â|s) || t(â|s))] < â¬. e8D)
The prior policy is then replaced with the new policy Ï, and the process is repeated.
# 4 METHOD
To enable more stable training and better exploit the natural information geometry of the parameter space, we propose to augment the entropy regularized expected reward objective OENT in (7) with a discounted relative entropy trust region around a prior policy ËÏ,
maximize E,[Ognr(7)]s.t. Es[G(s,7,7)] <e, (12)
where the discounted relative entropy is recursively deï¬ned as | 1707.01891#15 | Trust-PCL: An Off-Policy Trust Region Method for Continuous Control | Trust region methods, such as TRPO, are often used to stabilize policy
optimization algorithms in reinforcement learning (RL). While current trust
region strategies are effective for continuous control, they typically require
a prohibitively large amount of on-policy interaction with the environment. To
address this problem, we propose an off-policy trust region method, Trust-PCL.
The algorithm is the result of observing that the optimal policy and state
values of a maximum reward objective with a relative-entropy regularizer
satisfy a set of multi-step pathwise consistencies along any path. Thus,
Trust-PCL is able to maintain optimization stability while exploiting
off-policy data to improve sample efficiency. When evaluated on a number of
continuous control tasks, Trust-PCL improves the solution quality and sample
efficiency of TRPO. | http://arxiv.org/pdf/1707.01891 | Ofir Nachum, Mohammad Norouzi, Kelvin Xu, Dale Schuurmans | cs.AI | ICLR 2018 | null | cs.AI | 20170706 | 20180222 | [
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1707.01891 | 16 | where the discounted relative entropy is recursively deï¬ned as
G(s,7,7) = Ea, [log (als) â log #(a|s) + yG(s',7,7)] . (13)
This objective attempts to maximize entropy regularized expected reward while maintaining natural proximity to the previous policy. Although previous work has separately proposed to use relative entropy and entropy regularization, we ï¬nd that the two components serve different purposes, each of which is beneï¬cial: entropy regularization helps improve exploration, while the relative entropy improves stability and allows for a faster learning rate. This combination is a key novelty.
Using the method of Lagrange multipliers, we cast the constrained optimization problem in (13) into maximization of the following objective,
ORELENT(s, Ï) = OENT(s, Ï) â λG(s, Ï, ËÏ) . (14)
Again, the environment-wide objective is the expected per-state objective when states are sampled from interactions with the environment,
ORELENT(Ï) = Es[ORELENT(s, Ï)]. (15)
4.1 PATH CONSISTENCY WITH RELATIVE ENTROPY | 1707.01891#16 | Trust-PCL: An Off-Policy Trust Region Method for Continuous Control | Trust region methods, such as TRPO, are often used to stabilize policy
optimization algorithms in reinforcement learning (RL). While current trust
region strategies are effective for continuous control, they typically require
a prohibitively large amount of on-policy interaction with the environment. To
address this problem, we propose an off-policy trust region method, Trust-PCL.
The algorithm is the result of observing that the optimal policy and state
values of a maximum reward objective with a relative-entropy regularizer
satisfy a set of multi-step pathwise consistencies along any path. Thus,
Trust-PCL is able to maintain optimization stability while exploiting
off-policy data to improve sample efficiency. When evaluated on a number of
continuous control tasks, Trust-PCL improves the solution quality and sample
efficiency of TRPO. | http://arxiv.org/pdf/1707.01891 | Ofir Nachum, Mohammad Norouzi, Kelvin Xu, Dale Schuurmans | cs.AI | ICLR 2018 | null | cs.AI | 20170706 | 20180222 | [
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1707.01891 | 17 | ORELENT(Ï) = Es[ORELENT(s, Ï)]. (15)
4.1 PATH CONSISTENCY WITH RELATIVE ENTROPY
A key technical observation is that the ORELENT objective has a similar decomposition structure to OENT, and one can cast ORELENT as an entropy regularized expected reward objective with a set of transformed rewards, i.e.,
ORELENT(s, Ï) = â¼ OER(s, Ï) + (Ï + λ)H(s, Ï), (16)
4
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Published as a conference paper at ICLR 2018
â¼ OER(s, Ï) is an expected reward objective on a transformed reward distribution function where Ër(s, a) = r(s, a) + λ log ËÏ(a|s). Thus, in what follows, we derive a corresponding form of the multi-step path consistency in (10). Let Ïâ denote the optimal policy, deï¬ned as Ïâ = argmaxÏ ORELENT(Ï). As in PCL (Nachum et al., 2017), this optimal policy may be expressed as | 1707.01891#17 | Trust-PCL: An Off-Policy Trust Region Method for Continuous Control | Trust region methods, such as TRPO, are often used to stabilize policy
optimization algorithms in reinforcement learning (RL). While current trust
region strategies are effective for continuous control, they typically require
a prohibitively large amount of on-policy interaction with the environment. To
address this problem, we propose an off-policy trust region method, Trust-PCL.
The algorithm is the result of observing that the optimal policy and state
values of a maximum reward objective with a relative-entropy regularizer
satisfy a set of multi-step pathwise consistencies along any path. Thus,
Trust-PCL is able to maintain optimization stability while exploiting
off-policy data to improve sample efficiency. When evaluated on a number of
continuous control tasks, Trust-PCL improves the solution quality and sample
efficiency of TRPO. | http://arxiv.org/pdf/1707.01891 | Ofir Nachum, Mohammad Norouzi, Kelvin Xu, Dale Schuurmans | cs.AI | ICLR 2018 | null | cs.AI | 20170706 | 20180222 | [
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1707.01891 | 18 | Ej. 1~F (Se ae), Sega Lt > VV* (S41 s ails:) exn{ Fev (sesae), ia (se41)] = ak where V* are the softmax state values defined recursively as
Ex, .7(s¢,a),8¢41 [ht + WV (5 V*(s:) = (7 +A) tog f exp { Fuv(sea) sean lf + W"(se44)) \ da. (18) A T+X
We may re-arrange (17) to yield
V â(st) = EËrtâ¼Ër(st,at),st+1[Ërt â (Ï + λ) log Ïâ(at|st) + γV â(st+1)] = Ert,st+1[rt â (Ï + λ) log Ïâ(at|st) + λ log ËÏ(at+i|st+i) + γV â(st+1)]. (19) (20) | 1707.01891#18 | Trust-PCL: An Off-Policy Trust Region Method for Continuous Control | Trust region methods, such as TRPO, are often used to stabilize policy
optimization algorithms in reinforcement learning (RL). While current trust
region strategies are effective for continuous control, they typically require
a prohibitively large amount of on-policy interaction with the environment. To
address this problem, we propose an off-policy trust region method, Trust-PCL.
The algorithm is the result of observing that the optimal policy and state
values of a maximum reward objective with a relative-entropy regularizer
satisfy a set of multi-step pathwise consistencies along any path. Thus,
Trust-PCL is able to maintain optimization stability while exploiting
off-policy data to improve sample efficiency. When evaluated on a number of
continuous control tasks, Trust-PCL improves the solution quality and sample
efficiency of TRPO. | http://arxiv.org/pdf/1707.01891 | Ofir Nachum, Mohammad Norouzi, Kelvin Xu, Dale Schuurmans | cs.AI | ICLR 2018 | null | cs.AI | 20170706 | 20180222 | [
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1707.01891 | 19 | This is a single-step temporal consistency which may be extended to multiple steps by further ex- panding V*(s,41) on the RHS using the same identity. Thus, in general we have the following softmax temporal consistency constraint along any sequence of states defined by a starting state s; and a sequence of actions ay, ... , @t-4+dâ1: d-1
d-1 Vi(si) = E |y!V*(se4a) + 007 (reg â (7 + A) log (aryilseps) + Alog #(ar4i]8e4)) TepisSt+i â0 (21)
4.2 TRUST-PCL
We propose to train a parameterized policy Ïθ and value estimate VÏ to satisfy the multi-step con- sistencies in (21). Thus, we deï¬ne a consistency error for a sequence of states, actions, and rewards st:t+d â¡ (st, at, rt, . . . , st+dâ1, at+dâ1, rt+dâ1, st+d) sampled from the environment as
C(st:t+d, θ, Ï) = â VÏ(st) + γdVÏ(st+d) + | 1707.01891#19 | Trust-PCL: An Off-Policy Trust Region Method for Continuous Control | Trust region methods, such as TRPO, are often used to stabilize policy
optimization algorithms in reinforcement learning (RL). While current trust
region strategies are effective for continuous control, they typically require
a prohibitively large amount of on-policy interaction with the environment. To
address this problem, we propose an off-policy trust region method, Trust-PCL.
The algorithm is the result of observing that the optimal policy and state
values of a maximum reward objective with a relative-entropy regularizer
satisfy a set of multi-step pathwise consistencies along any path. Thus,
Trust-PCL is able to maintain optimization stability while exploiting
off-policy data to improve sample efficiency. When evaluated on a number of
continuous control tasks, Trust-PCL improves the solution quality and sample
efficiency of TRPO. | http://arxiv.org/pdf/1707.01891 | Ofir Nachum, Mohammad Norouzi, Kelvin Xu, Dale Schuurmans | cs.AI | ICLR 2018 | null | cs.AI | 20170706 | 20180222 | [
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1707.01891 | 20 | C(st:t+d, θ, Ï) = â VÏ(st) + γdVÏ(st+d) +
= âVa(se) + Â¥V(sta) + d-1 (22) SO! (rete = (7 + A) log ro (aeqilseps) + Alog mg (ae4ilse4a)) - i=0
We aim to minimize the squared consistency error on every sub-trajectory of length d. That is, the loss for a given batch of episodes (or sub-episodes) S = {s(k) 0:Tk
B T,-1 £(S,0,6) => > C(s{), 1.9.6)". (23) k=1 t=0
t=0 We perform gradient descent on θ and Ï to minimize this loss. In practice, we have found that it is beneï¬cial to learn the parameter Ï at least as fast as θ, and accordingly, given a mini-batch of episodes we perform a single gradient update on θ and possibly multiple gradient updates on Ï (see Appendix for details). | 1707.01891#20 | Trust-PCL: An Off-Policy Trust Region Method for Continuous Control | Trust region methods, such as TRPO, are often used to stabilize policy
optimization algorithms in reinforcement learning (RL). While current trust
region strategies are effective for continuous control, they typically require
a prohibitively large amount of on-policy interaction with the environment. To
address this problem, we propose an off-policy trust region method, Trust-PCL.
The algorithm is the result of observing that the optimal policy and state
values of a maximum reward objective with a relative-entropy regularizer
satisfy a set of multi-step pathwise consistencies along any path. Thus,
Trust-PCL is able to maintain optimization stability while exploiting
off-policy data to improve sample efficiency. When evaluated on a number of
continuous control tasks, Trust-PCL improves the solution quality and sample
efficiency of TRPO. | http://arxiv.org/pdf/1707.01891 | Ofir Nachum, Mohammad Norouzi, Kelvin Xu, Dale Schuurmans | cs.AI | ICLR 2018 | null | cs.AI | 20170706 | 20180222 | [
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1707.01891 | 21 | In principle, the mini-batch S may be taken from either on-policy or off-policy trajectories. In our implementation, we utilized a replay buffer prioritized by recency. As episodes (or sub-episodes) are sampled from the environment they are placed in a replay buffer and a priority p(s0:T ) is given to a trajectory s0:T equivalent to the current training step. Then, to sample a batch for training, B episodes are sampled from the replay buffer proportional to exponentiated priority exp{βp(s0:T )} for some hyperparameter β ⥠0.
For the prior policy ÏËθ, we use a lagged geometric mean of the parameters. At each training step, we update Ëθ â αËθ + (1 â α)θ. Thus on average our training scheme attempts to maximize entropy regularized expected reward while penalizing divergence from a policy roughly 1/(1 â α) training steps in the past.
5
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.
Published as a conference paper at ICLR 2018
4.3 AUTOMATIC TUNING OF THE LAGRANGE MULTIPLIER λ | 1707.01891#21 | Trust-PCL: An Off-Policy Trust Region Method for Continuous Control | Trust region methods, such as TRPO, are often used to stabilize policy
optimization algorithms in reinforcement learning (RL). While current trust
region strategies are effective for continuous control, they typically require
a prohibitively large amount of on-policy interaction with the environment. To
address this problem, we propose an off-policy trust region method, Trust-PCL.
The algorithm is the result of observing that the optimal policy and state
values of a maximum reward objective with a relative-entropy regularizer
satisfy a set of multi-step pathwise consistencies along any path. Thus,
Trust-PCL is able to maintain optimization stability while exploiting
off-policy data to improve sample efficiency. When evaluated on a number of
continuous control tasks, Trust-PCL improves the solution quality and sample
efficiency of TRPO. | http://arxiv.org/pdf/1707.01891 | Ofir Nachum, Mohammad Norouzi, Kelvin Xu, Dale Schuurmans | cs.AI | ICLR 2018 | null | cs.AI | 20170706 | 20180222 | [
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1707.01891 | 22 | 5
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.
Published as a conference paper at ICLR 2018
4.3 AUTOMATIC TUNING OF THE LAGRANGE MULTIPLIER λ
The use of a relative entropy regularizer as a penalty rather than a constraint introduces several difï¬culties. The hyperparameter λ must necessarily adapt to the distribution of rewards. Thus, λ must be tuned not only to each environment but also during training on a single environment, since the observed reward distribution changes as the agentâs behavior policy improves. Using a constraint form of the regularizer is more desirable, and others have advocated its use in practice (Schulman et al., 2015) speciï¬cally to robustly allow larger updates during training.
To this end, we propose to redirect the hyperparameter tuning from \ to e. Specifically, we present a method which, given a desired hard constraint on the relative entropy defined by â¬, approximates the equivalent penalty coefficient A(c). This is a key novelty of our work and is distinct from previous attempts at automatically tuning a regularizing coefficient, which iteratively increase and decrease the coefficient based on observed training behavior (Schulman et al.| 2017b} Heess et al} 2017). | 1707.01891#22 | Trust-PCL: An Off-Policy Trust Region Method for Continuous Control | Trust region methods, such as TRPO, are often used to stabilize policy
optimization algorithms in reinforcement learning (RL). While current trust
region strategies are effective for continuous control, they typically require
a prohibitively large amount of on-policy interaction with the environment. To
address this problem, we propose an off-policy trust region method, Trust-PCL.
The algorithm is the result of observing that the optimal policy and state
values of a maximum reward objective with a relative-entropy regularizer
satisfy a set of multi-step pathwise consistencies along any path. Thus,
Trust-PCL is able to maintain optimization stability while exploiting
off-policy data to improve sample efficiency. When evaluated on a number of
continuous control tasks, Trust-PCL improves the solution quality and sample
efficiency of TRPO. | http://arxiv.org/pdf/1707.01891 | Ofir Nachum, Mohammad Norouzi, Kelvin Xu, Dale Schuurmans | cs.AI | ICLR 2018 | null | cs.AI | 20170706 | 20180222 | [
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1707.01891 | 23 | We restrict our analysis to the undiscounted setting γ = 1 with entropy regularizer Ï = 0. Addi- tionally, we assume deterministic, ï¬nite-horizon environment dynamics. An additional assumption we make is that the expected KL-divergence over states is well-approximated by the KL-divergence starting from the unique initial state s0. Although in our experiments these restrictive assumptions are not met, we still found our method to perform well for adapting λ during training.
In this setting the optimal policy of (14) is proportional to exponentiated scaled reward. Speciï¬cally, for a full episode s0:T = (s0, a0, r0, . . . , sT â1, aT â1, rT â1, sT ), we have
1° (so) x Aso) exp {SCOT 04)
where (sor) = an t(a;|s;) and R(so:r) = ye a r;. The normalization factor of 7* is
a r;. The normalization factor of 7* is { Rison) \ .
Z = Es0:T â¼ËÏ exp . (25) | 1707.01891#23 | Trust-PCL: An Off-Policy Trust Region Method for Continuous Control | Trust region methods, such as TRPO, are often used to stabilize policy
optimization algorithms in reinforcement learning (RL). While current trust
region strategies are effective for continuous control, they typically require
a prohibitively large amount of on-policy interaction with the environment. To
address this problem, we propose an off-policy trust region method, Trust-PCL.
The algorithm is the result of observing that the optimal policy and state
values of a maximum reward objective with a relative-entropy regularizer
satisfy a set of multi-step pathwise consistencies along any path. Thus,
Trust-PCL is able to maintain optimization stability while exploiting
off-policy data to improve sample efficiency. When evaluated on a number of
continuous control tasks, Trust-PCL improves the solution quality and sample
efficiency of TRPO. | http://arxiv.org/pdf/1707.01891 | Ofir Nachum, Mohammad Norouzi, Kelvin Xu, Dale Schuurmans | cs.AI | ICLR 2018 | null | cs.AI | 20170706 | 20180222 | [
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1707.01891 | 24 | a r;. The normalization factor of 7* is { Rison) \ .
Z = Es0:T â¼ËÏ exp . (25)
We would like to approximate the trajectory-wide KL-divergence between Ïâ and ËÏ. We may ex- press the KL-divergence analytically:
KL(n* ||) = Eyopvn- [oe Ur) (26) T(Sorr
=Egy.par* [As sor) _ toe Z] (27)
â log Z + Esgnws [As (so:r) ote) (28) 7(So:7)
# [As (so:r) Rlosn) Xr )
Rlosn) Xr âlogZ + Es. px% ) exp{R(s0r)/A â log 2)| . (29)
Since all expectations are with respect to ËÏ, this quantity is tractable to approximate given episodes sampled from ËÏ | 1707.01891#24 | Trust-PCL: An Off-Policy Trust Region Method for Continuous Control | Trust region methods, such as TRPO, are often used to stabilize policy
optimization algorithms in reinforcement learning (RL). While current trust
region strategies are effective for continuous control, they typically require
a prohibitively large amount of on-policy interaction with the environment. To
address this problem, we propose an off-policy trust region method, Trust-PCL.
The algorithm is the result of observing that the optimal policy and state
values of a maximum reward objective with a relative-entropy regularizer
satisfy a set of multi-step pathwise consistencies along any path. Thus,
Trust-PCL is able to maintain optimization stability while exploiting
off-policy data to improve sample efficiency. When evaluated on a number of
continuous control tasks, Trust-PCL improves the solution quality and sample
efficiency of TRPO. | http://arxiv.org/pdf/1707.01891 | Ofir Nachum, Mohammad Norouzi, Kelvin Xu, Dale Schuurmans | cs.AI | ICLR 2018 | null | cs.AI | 20170706 | 20180222 | [
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1707.01891 | 25 | Since all expectations are with respect to ËÏ, this quantity is tractable to approximate given episodes sampled from ËÏ
Therefore, in Trust-PCL, given a set of episodes sampled from the prior policy 73 and a desired maximum divergence eâ¬, we can perform a simple line search to find a suitable \(e) which yields KL(x"*||79) as close as possible to â¬. The preceding analysis provided a method to determine \(¢) given a desired maximum divergence e. However, there is still a question of whether ¢ should change during training. Indeed, as episodes may possibly i increase in length, K L(7*||7) naturally increases when compared to the average per- state K L(x*(â|s)||7(â|s)), and vice versa for decreasing length. Thus, in practice, given an ⬠and a set of sampled episodes S= {s\*) Te })_, we approximate the best \ which yields a maximum divergence of < < k=1 Lk- This makes it so that ⬠corresponds more to a constraint on the length- averaged KL- divergence.
To avoid incurring a prohibitively large number of interactions with the environment for each pa- rameter update, in practice we use the last 100 episodes as the set of sampled episodes S. While
6
Published as a conference paper at ICLR 2018 | 1707.01891#25 | Trust-PCL: An Off-Policy Trust Region Method for Continuous Control | Trust region methods, such as TRPO, are often used to stabilize policy
optimization algorithms in reinforcement learning (RL). While current trust
region strategies are effective for continuous control, they typically require
a prohibitively large amount of on-policy interaction with the environment. To
address this problem, we propose an off-policy trust region method, Trust-PCL.
The algorithm is the result of observing that the optimal policy and state
values of a maximum reward objective with a relative-entropy regularizer
satisfy a set of multi-step pathwise consistencies along any path. Thus,
Trust-PCL is able to maintain optimization stability while exploiting
off-policy data to improve sample efficiency. When evaluated on a number of
continuous control tasks, Trust-PCL improves the solution quality and sample
efficiency of TRPO. | http://arxiv.org/pdf/1707.01891 | Ofir Nachum, Mohammad Norouzi, Kelvin Xu, Dale Schuurmans | cs.AI | ICLR 2018 | null | cs.AI | 20170706 | 20180222 | [
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},
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"id": "1702.08165"
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"id": "1611.01224"
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},
{
"id": "1706.00387"
}
] |
1707.01891 | 26 | 6
Published as a conference paper at ICLR 2018
this is not exactly the same as sampling episodes from ÏËθ, it is not too far off since ÏËθ is a lagged version of the online policy Ïθ. Moreover, we observed this protocol to work well in practice. A more sophisticated and accurate protocol may be derived by weighting the episodes according to the importance weights corresponding to their true sampling distribution.
# 5 EXPERIMENTS
We evaluate Trust-PCL against TRPO on a number of benchmark tasks. We choose TRPO as a base- line since it is a standard algorithm known to achieve state-of-the-art performance on the continuous control tasks we consider (see e.g., leaderboard results on the OpenAI Gym website (Brockman et al., 2016)). We ï¬nd that Trust-PCL can match or improve upon TRPOâs performance in terms of both average reward and sample efï¬ciency.
5.1 SETUP | 1707.01891#26 | Trust-PCL: An Off-Policy Trust Region Method for Continuous Control | Trust region methods, such as TRPO, are often used to stabilize policy
optimization algorithms in reinforcement learning (RL). While current trust
region strategies are effective for continuous control, they typically require
a prohibitively large amount of on-policy interaction with the environment. To
address this problem, we propose an off-policy trust region method, Trust-PCL.
The algorithm is the result of observing that the optimal policy and state
values of a maximum reward objective with a relative-entropy regularizer
satisfy a set of multi-step pathwise consistencies along any path. Thus,
Trust-PCL is able to maintain optimization stability while exploiting
off-policy data to improve sample efficiency. When evaluated on a number of
continuous control tasks, Trust-PCL improves the solution quality and sample
efficiency of TRPO. | http://arxiv.org/pdf/1707.01891 | Ofir Nachum, Mohammad Norouzi, Kelvin Xu, Dale Schuurmans | cs.AI | ICLR 2018 | null | cs.AI | 20170706 | 20180222 | [
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"id": "1606.01540"
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}
] |
1707.01891 | 27 | 5.1 SETUP
We chose a number of control tasks available from OpenAI Gym (Brockman et al., 2016). The ï¬rst task, Acrobot, is a discrete-control task, while the remaining tasks (HalfCheetah, Swimmer, Hopper, Walker2d, and Ant) are well-known continuous-control tasks utilizing the MuJoCo envi- ronment (Todorov et al., 2012).
For TRPO we trained using batches of Q = 25, 000 steps (12, 500 for Acrobot), which is the approximate batch size used by other implementations (Duan et al., 2016; Schulman, 2017). Thus, at each training iteration, TRPO samples 25, 000 steps using the policy ÏËθ and then takes a single step within a KL-ball to yield a new Ïθ. | 1707.01891#27 | Trust-PCL: An Off-Policy Trust Region Method for Continuous Control | Trust region methods, such as TRPO, are often used to stabilize policy
optimization algorithms in reinforcement learning (RL). While current trust
region strategies are effective for continuous control, they typically require
a prohibitively large amount of on-policy interaction with the environment. To
address this problem, we propose an off-policy trust region method, Trust-PCL.
The algorithm is the result of observing that the optimal policy and state
values of a maximum reward objective with a relative-entropy regularizer
satisfy a set of multi-step pathwise consistencies along any path. Thus,
Trust-PCL is able to maintain optimization stability while exploiting
off-policy data to improve sample efficiency. When evaluated on a number of
continuous control tasks, Trust-PCL improves the solution quality and sample
efficiency of TRPO. | http://arxiv.org/pdf/1707.01891 | Ofir Nachum, Mohammad Norouzi, Kelvin Xu, Dale Schuurmans | cs.AI | ICLR 2018 | null | cs.AI | 20170706 | 20180222 | [
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1707.01891 | 28 | Trust-PCL is off-policy, so to evaluate its performance we alternate between collecting experience and training on batches of experience sampled from the replay buffer. Speciï¬cally, we alternate between collecting P = 10 steps from the environment and performing a single gradient step based on a batch of size Q = 64 sub-episodes of length P from the replay buffer, with a recency weight of β = 0.001 on the sampling distribution of the replay buffer. To maintain stability we use α = 0.99 and we modiï¬ed the loss from squared loss to Huber loss on the consistency error. Since our policy is parameterized by a unimodal Gaussian, it is impossible for it to satisfy all path consistencies, and so we found this crucial for stability.
For each of the variants and for each environment, we performed a hyperparameter search to ï¬nd the best hyperparameters. The plots presented here show the reward achieved during training on the best hyperparameters averaged over the best 4 seeds of 5 randomly seeded training runs. Note that this reward is based on greedy actions (rather than random sampling). | 1707.01891#28 | Trust-PCL: An Off-Policy Trust Region Method for Continuous Control | Trust region methods, such as TRPO, are often used to stabilize policy
optimization algorithms in reinforcement learning (RL). While current trust
region strategies are effective for continuous control, they typically require
a prohibitively large amount of on-policy interaction with the environment. To
address this problem, we propose an off-policy trust region method, Trust-PCL.
The algorithm is the result of observing that the optimal policy and state
values of a maximum reward objective with a relative-entropy regularizer
satisfy a set of multi-step pathwise consistencies along any path. Thus,
Trust-PCL is able to maintain optimization stability while exploiting
off-policy data to improve sample efficiency. When evaluated on a number of
continuous control tasks, Trust-PCL improves the solution quality and sample
efficiency of TRPO. | http://arxiv.org/pdf/1707.01891 | Ofir Nachum, Mohammad Norouzi, Kelvin Xu, Dale Schuurmans | cs.AI | ICLR 2018 | null | cs.AI | 20170706 | 20180222 | [
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1707.01891 | 29 | Experiments were performed using Tensorï¬ow (Abadi et al., 2016). Although each training step of Trust-PCL (a simple gradient step) is considerably faster than TRPO, we found that this does not have an overall effect on the run time of our implementation, due to a combination of the fact that each environment step is used in multiple training steps of Trust-PCL and that a majority of the run time is spent interacting with the environment. A detailed description of our implementation and hyperparameter search is available in the Appendix.
5.2 RESULTS
We present the reward over training of Trust-PCL and TRPO in Figure 1. We ï¬nd that Trust-PCL can match or beat the performance of TRPO across all environments in terms of both ï¬nal reward and sample efï¬ciency. These results are especially signiï¬cant on the harder tasks (Walker2d and Ant). We additionally present our results compared to other published results in Table 1. We ï¬nd that even when comparing across different implementations, Trust-PCL can match or beat the state-of-the-art.
5.2.1 HYPERPARAMETER ANALYSIS | 1707.01891#29 | Trust-PCL: An Off-Policy Trust Region Method for Continuous Control | Trust region methods, such as TRPO, are often used to stabilize policy
optimization algorithms in reinforcement learning (RL). While current trust
region strategies are effective for continuous control, they typically require
a prohibitively large amount of on-policy interaction with the environment. To
address this problem, we propose an off-policy trust region method, Trust-PCL.
The algorithm is the result of observing that the optimal policy and state
values of a maximum reward objective with a relative-entropy regularizer
satisfy a set of multi-step pathwise consistencies along any path. Thus,
Trust-PCL is able to maintain optimization stability while exploiting
off-policy data to improve sample efficiency. When evaluated on a number of
continuous control tasks, Trust-PCL improves the solution quality and sample
efficiency of TRPO. | http://arxiv.org/pdf/1707.01891 | Ofir Nachum, Mohammad Norouzi, Kelvin Xu, Dale Schuurmans | cs.AI | ICLR 2018 | null | cs.AI | 20170706 | 20180222 | [
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1707.01891 | 30 | 5.2.1 HYPERPARAMETER ANALYSIS
The most important hyperparameter in our method is â¬, which determines the size of the trust region and thus has a critical role in the stability of the algorithm. To showcase this effect, we present the reward during training for several different values of ⬠in Figure [2] As ⬠increases, instability in- creases as well, eventually having an adverse effect on the agentâs ability to achieve optimal reward.
7
Published as a conference paper at ICLR 2018
Acrobot HalfCheetah Swimmer Hopper Walker2d Ant
Figure 1: The results of Trust-PCL against a TRPO baseline. Each plot shows average greedy reward with single standard deviation error intervals capped at the min and max across 4 best of 5 randomly seeded training runs after choosing best hyperparameters. The x-axis shows millions of environment steps. We observe that Trust-PCL is consistently able to match and, in many cases, beat TRPOâs performance both in terms of reward and sample efï¬ciency.
Hopper Walker2d | 1707.01891#30 | Trust-PCL: An Off-Policy Trust Region Method for Continuous Control | Trust region methods, such as TRPO, are often used to stabilize policy
optimization algorithms in reinforcement learning (RL). While current trust
region strategies are effective for continuous control, they typically require
a prohibitively large amount of on-policy interaction with the environment. To
address this problem, we propose an off-policy trust region method, Trust-PCL.
The algorithm is the result of observing that the optimal policy and state
values of a maximum reward objective with a relative-entropy regularizer
satisfy a set of multi-step pathwise consistencies along any path. Thus,
Trust-PCL is able to maintain optimization stability while exploiting
off-policy data to improve sample efficiency. When evaluated on a number of
continuous control tasks, Trust-PCL improves the solution quality and sample
efficiency of TRPO. | http://arxiv.org/pdf/1707.01891 | Ofir Nachum, Mohammad Norouzi, Kelvin Xu, Dale Schuurmans | cs.AI | ICLR 2018 | null | cs.AI | 20170706 | 20180222 | [
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1707.01891 | 31 | Hopper Walker2d
Figure 2: The results of Trust-PCL across several values of ¢, defining the size of the trust re- gion. Each plot shows average greedy reward across 4 best of 5 randomly seeded training runs after choosing best hyperparameters. The x-axis shows millions of environment steps. We observe that instability increases with â¬, thus concluding that the use of trust region is crucial.
Note that standard PCL standard PCL would fail (Nachum et al.|/2017) corresponds to ⬠â oo (that is, \ = 0). Therefore, in the se environments, and the use of trust region is crucial. | 1707.01891#31 | Trust-PCL: An Off-Policy Trust Region Method for Continuous Control | Trust region methods, such as TRPO, are often used to stabilize policy
optimization algorithms in reinforcement learning (RL). While current trust
region strategies are effective for continuous control, they typically require
a prohibitively large amount of on-policy interaction with the environment. To
address this problem, we propose an off-policy trust region method, Trust-PCL.
The algorithm is the result of observing that the optimal policy and state
values of a maximum reward objective with a relative-entropy regularizer
satisfy a set of multi-step pathwise consistencies along any path. Thus,
Trust-PCL is able to maintain optimization stability while exploiting
off-policy data to improve sample efficiency. When evaluated on a number of
continuous control tasks, Trust-PCL improves the solution quality and sample
efficiency of TRPO. | http://arxiv.org/pdf/1707.01891 | Ofir Nachum, Mohammad Norouzi, Kelvin Xu, Dale Schuurmans | cs.AI | ICLR 2018 | null | cs.AI | 20170706 | 20180222 | [
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1707.01891 | 32 | The main advantage of Trust-PCL over existing trust region methods for continuous control is its ability to learn in an off-policy manner. The degree to which Trust-PCL is off-policy is determined by a combination of the hyparparameters α, β, and P . To evaluate the importance of training off-policy, we evaluate Trust-PCL with a hyperparameter setting that is more on-policy. We set α = 0.95, β = 0.1, and P = 1, 000. In this setting, we also use large batches of Q = 25 episodes of length P (a total of 25, 000 environment steps per batch). Figure 3 shows the results of Trust-PCL with our original parameters and this new setting. We note a dramatic advantage in sample efï¬ciency when using off-policy training. Although Trust-PCL (on-policy) can achieve state-of-the-art reward performance, it requires an exorbitant amount of experience. On the other hand, Trust-PCL (off8
Published as a conference paper at ICLR 2018
Hopper Walker2d | 1707.01891#32 | Trust-PCL: An Off-Policy Trust Region Method for Continuous Control | Trust region methods, such as TRPO, are often used to stabilize policy
optimization algorithms in reinforcement learning (RL). While current trust
region strategies are effective for continuous control, they typically require
a prohibitively large amount of on-policy interaction with the environment. To
address this problem, we propose an off-policy trust region method, Trust-PCL.
The algorithm is the result of observing that the optimal policy and state
values of a maximum reward objective with a relative-entropy regularizer
satisfy a set of multi-step pathwise consistencies along any path. Thus,
Trust-PCL is able to maintain optimization stability while exploiting
off-policy data to improve sample efficiency. When evaluated on a number of
continuous control tasks, Trust-PCL improves the solution quality and sample
efficiency of TRPO. | http://arxiv.org/pdf/1707.01891 | Ofir Nachum, Mohammad Norouzi, Kelvin Xu, Dale Schuurmans | cs.AI | ICLR 2018 | null | cs.AI | 20170706 | 20180222 | [
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1707.01891 | 33 | Published as a conference paper at ICLR 2018
Hopper Walker2d
Figure 3: The results of Trust-PCL varying the degree of on/off-policy. We see that Trust-PCL (on-policy) has a behavior similar to TRPO, achieving good ï¬nal reward but requiring an exorbitant number of experience collection. When collecting less experience per training step in Trust-PCL (off-policy), we are able to improve sample efï¬ciency while still achieving a competitive ï¬nal re- ward.
Domain HalfCheetah Swimmer Hopper Walker2d Ant TRPO-GAE 4871.36 137.25 3765.78 6028.73 2918.25 TRPO (rllab) 2889 â â 1487 1520 TRPO (ours) 4343.6 288.1 3516.7 2838.4 4347.5 Trust-PCL 7057.1 297.0 3804.9 5027.2 6104.2 IPG 4767 â â 3047 4415 | 1707.01891#33 | Trust-PCL: An Off-Policy Trust Region Method for Continuous Control | Trust region methods, such as TRPO, are often used to stabilize policy
optimization algorithms in reinforcement learning (RL). While current trust
region strategies are effective for continuous control, they typically require
a prohibitively large amount of on-policy interaction with the environment. To
address this problem, we propose an off-policy trust region method, Trust-PCL.
The algorithm is the result of observing that the optimal policy and state
values of a maximum reward objective with a relative-entropy regularizer
satisfy a set of multi-step pathwise consistencies along any path. Thus,
Trust-PCL is able to maintain optimization stability while exploiting
off-policy data to improve sample efficiency. When evaluated on a number of
continuous control tasks, Trust-PCL improves the solution quality and sample
efficiency of TRPO. | http://arxiv.org/pdf/1707.01891 | Ofir Nachum, Mohammad Norouzi, Kelvin Xu, Dale Schuurmans | cs.AI | ICLR 2018 | null | cs.AI | 20170706 | 20180222 | [
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1707.01891 | 34 | Table 1: Results for best average reward in the ï¬rst 10M steps of training for our implementations (TRPO (ours) and Trust-PCL) and external implementations. TRPO-GAE are results of Schulman (2017) available on the OpenAI Gym website. TRPO (rllab) and IPG are taken from Gu et al. (2017b). These results are each on different setups with different hyperparameter searches and in some cases different evaluation protocols (e.g.,TRPO (rllab) and IPG were run with a simple linear value network instead of the two-hidden layer network we use). Thus, it is not possible to make any deï¬nitive claims based on this data. However, we do conclude that our results are overall competitive with state-of-the-art external implementations.
policy) can be competitive in terms of reward while providing a signiï¬cant improvement in sample efï¬ciency. | 1707.01891#34 | Trust-PCL: An Off-Policy Trust Region Method for Continuous Control | Trust region methods, such as TRPO, are often used to stabilize policy
optimization algorithms in reinforcement learning (RL). While current trust
region strategies are effective for continuous control, they typically require
a prohibitively large amount of on-policy interaction with the environment. To
address this problem, we propose an off-policy trust region method, Trust-PCL.
The algorithm is the result of observing that the optimal policy and state
values of a maximum reward objective with a relative-entropy regularizer
satisfy a set of multi-step pathwise consistencies along any path. Thus,
Trust-PCL is able to maintain optimization stability while exploiting
off-policy data to improve sample efficiency. When evaluated on a number of
continuous control tasks, Trust-PCL improves the solution quality and sample
efficiency of TRPO. | http://arxiv.org/pdf/1707.01891 | Ofir Nachum, Mohammad Norouzi, Kelvin Xu, Dale Schuurmans | cs.AI | ICLR 2018 | null | cs.AI | 20170706 | 20180222 | [
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1707.01891 | 35 | policy) can be competitive in terms of reward while providing a signiï¬cant improvement in sample efï¬ciency.
One last hyperparameter is Ï , determining the degree of exploration. Anecdotally, we found Ï to not be of high importance for the tasks we evaluated. Indeed many of our best results use Ï = 0. Including Ï > 0 had a marginal effect, at best. The reason for this is likely due to the tasks themselves. Indeed, other works which focus on exploration in continuous control have found the need to propose exploration-advanageous variants of these standard benchmarks (Haarnoja et al., 2017; Houthooft et al., 2016).
# 6 CONCLUSION | 1707.01891#35 | Trust-PCL: An Off-Policy Trust Region Method for Continuous Control | Trust region methods, such as TRPO, are often used to stabilize policy
optimization algorithms in reinforcement learning (RL). While current trust
region strategies are effective for continuous control, they typically require
a prohibitively large amount of on-policy interaction with the environment. To
address this problem, we propose an off-policy trust region method, Trust-PCL.
The algorithm is the result of observing that the optimal policy and state
values of a maximum reward objective with a relative-entropy regularizer
satisfy a set of multi-step pathwise consistencies along any path. Thus,
Trust-PCL is able to maintain optimization stability while exploiting
off-policy data to improve sample efficiency. When evaluated on a number of
continuous control tasks, Trust-PCL improves the solution quality and sample
efficiency of TRPO. | http://arxiv.org/pdf/1707.01891 | Ofir Nachum, Mohammad Norouzi, Kelvin Xu, Dale Schuurmans | cs.AI | ICLR 2018 | null | cs.AI | 20170706 | 20180222 | [
{
"id": "1605.08695"
},
{
"id": "1707.06347"
},
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"id": "1702.08165"
},
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"id": "1704.06440"
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"id": "1509.02971"
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"id": "1707.02286"
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"id": "1611.01224"
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{
"id": "1606.01540"
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}
] |
1707.01891 | 36 | # 6 CONCLUSION
We have presented Trust-PCL, an off-policy algorithm employing a relative-entropy penalty to im- pose a trust region on a maximum reward objective. We found that Trust-PCL can perform well on a set of standard control tasks, improving upon TRPO both in terms of average reward and sample efï¬- ciency. Our best results on Trust-PCL are able to maintain the stability and solution quality of TRPO while approaching the sample-efï¬ciency of value-based methods (see e.g., Metz et al. (2017)). This gives hope that the goal of achieving both stability and sample-efï¬ciency without trading-off one for the other is attainable in a single unifying RL algorithm.
9
Published as a conference paper at ICLR 2018
# 7 ACKNOWLEDGMENT
We thank Matthew Johnson, Luke Metz, Shane Gu, and the Google Brain team for insightful com- ments and discussions.
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optimization algorithms in reinforcement learning (RL). While current trust
region strategies are effective for continuous control, they typically require
a prohibitively large amount of on-policy interaction with the environment. To
address this problem, we propose an off-policy trust region method, Trust-PCL.
The algorithm is the result of observing that the optimal policy and state
values of a maximum reward objective with a relative-entropy regularizer
satisfy a set of multi-step pathwise consistencies along any path. Thus,
Trust-PCL is able to maintain optimization stability while exploiting
off-policy data to improve sample efficiency. When evaluated on a number of
continuous control tasks, Trust-PCL improves the solution quality and sample
efficiency of TRPO. | http://arxiv.org/pdf/1707.01891 | Ofir Nachum, Mohammad Norouzi, Kelvin Xu, Dale Schuurmans | cs.AI | ICLR 2018 | null | cs.AI | 20170706 | 20180222 | [
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},
{
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"id": "1702.08165"
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{
"id": "1704.06440"
},
{
"id": "1509.02971"
},
{
"id": "1707.02286"
},
{
"id": "1611.01224"
},
{
"id": "1606.01540"
},
{
"id": "1706.00387"
}
] |
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optimization algorithms in reinforcement learning (RL). While current trust
region strategies are effective for continuous control, they typically require
a prohibitively large amount of on-policy interaction with the environment. To
address this problem, we propose an off-policy trust region method, Trust-PCL.
The algorithm is the result of observing that the optimal policy and state
values of a maximum reward objective with a relative-entropy regularizer
satisfy a set of multi-step pathwise consistencies along any path. Thus,
Trust-PCL is able to maintain optimization stability while exploiting
off-policy data to improve sample efficiency. When evaluated on a number of
continuous control tasks, Trust-PCL improves the solution quality and sample
efficiency of TRPO. | http://arxiv.org/pdf/1707.01891 | Ofir Nachum, Mohammad Norouzi, Kelvin Xu, Dale Schuurmans | cs.AI | ICLR 2018 | null | cs.AI | 20170706 | 20180222 | [
{
"id": "1605.08695"
},
{
"id": "1707.06347"
},
{
"id": "1702.08165"
},
{
"id": "1704.06440"
},
{
"id": "1509.02971"
},
{
"id": "1707.02286"
},
{
"id": "1611.01224"
},
{
"id": "1606.01540"
},
{
"id": "1706.00387"
}
] |
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optimization algorithms in reinforcement learning (RL). While current trust
region strategies are effective for continuous control, they typically require
a prohibitively large amount of on-policy interaction with the environment. To
address this problem, we propose an off-policy trust region method, Trust-PCL.
The algorithm is the result of observing that the optimal policy and state
values of a maximum reward objective with a relative-entropy regularizer
satisfy a set of multi-step pathwise consistencies along any path. Thus,
Trust-PCL is able to maintain optimization stability while exploiting
off-policy data to improve sample efficiency. When evaluated on a number of
continuous control tasks, Trust-PCL improves the solution quality and sample
efficiency of TRPO. | http://arxiv.org/pdf/1707.01891 | Ofir Nachum, Mohammad Norouzi, Kelvin Xu, Dale Schuurmans | cs.AI | ICLR 2018 | null | cs.AI | 20170706 | 20180222 | [
{
"id": "1605.08695"
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"id": "1707.06347"
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] |
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Luke Metz, Julian Ibarz, Navdeep Jaitly, and James Davidson. Discrete sequential prediction of continuous actions for deep RL. CoRR, abs/1705.05035, 2017. URL http://arxiv.org/ abs/1705.05035. | 1707.01891#39 | Trust-PCL: An Off-Policy Trust Region Method for Continuous Control | Trust region methods, such as TRPO, are often used to stabilize policy
optimization algorithms in reinforcement learning (RL). While current trust
region strategies are effective for continuous control, they typically require
a prohibitively large amount of on-policy interaction with the environment. To
address this problem, we propose an off-policy trust region method, Trust-PCL.
The algorithm is the result of observing that the optimal policy and state
values of a maximum reward objective with a relative-entropy regularizer
satisfy a set of multi-step pathwise consistencies along any path. Thus,
Trust-PCL is able to maintain optimization stability while exploiting
off-policy data to improve sample efficiency. When evaluated on a number of
continuous control tasks, Trust-PCL improves the solution quality and sample
efficiency of TRPO. | http://arxiv.org/pdf/1707.01891 | Ofir Nachum, Mohammad Norouzi, Kelvin Xu, Dale Schuurmans | cs.AI | ICLR 2018 | null | cs.AI | 20170706 | 20180222 | [
{
"id": "1605.08695"
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{
"id": "1707.06347"
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"id": "1702.08165"
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"id": "1704.06440"
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{
"id": "1509.02971"
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"id": "1707.02286"
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"id": "1611.01224"
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"id": "1606.01540"
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1707.01891 | 40 | Volodymyr Mnih, Koray Kavukcuoglu, David Silver, Alex Graves, Ioannis Antonoglou, Daan Wier- stra, and Martin A. Riedmiller. Playing atari with deep reinforcement learning. arXiv:1312.5602, 2013.
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Oï¬r Nachum, Mohammad Norouzi, Kelvin Xu, and Dale Schuurmans. Bridging the gap between value and policy based reinforcement learning. CoRR, abs/1702.08892, 2017. URL http: //arxiv.org/abs/1702.08892.
Mohammad Norouzi, Samy Bengio, Zhifeng Chen, Navdeep Jaitly, Mike Schuster, Yonghui Wu, and Dale Schuurmans. Reward augmented maximum likelihood for neural structured prediction. NIPS, 2016.
Neal Parikh, Stephen Boyd, et al. Proximal algorithms. Foundations and Trends®) in Optimization, 1(3):127-239, 2014. | 1707.01891#40 | Trust-PCL: An Off-Policy Trust Region Method for Continuous Control | Trust region methods, such as TRPO, are often used to stabilize policy
optimization algorithms in reinforcement learning (RL). While current trust
region strategies are effective for continuous control, they typically require
a prohibitively large amount of on-policy interaction with the environment. To
address this problem, we propose an off-policy trust region method, Trust-PCL.
The algorithm is the result of observing that the optimal policy and state
values of a maximum reward objective with a relative-entropy regularizer
satisfy a set of multi-step pathwise consistencies along any path. Thus,
Trust-PCL is able to maintain optimization stability while exploiting
off-policy data to improve sample efficiency. When evaluated on a number of
continuous control tasks, Trust-PCL improves the solution quality and sample
efficiency of TRPO. | http://arxiv.org/pdf/1707.01891 | Ofir Nachum, Mohammad Norouzi, Kelvin Xu, Dale Schuurmans | cs.AI | ICLR 2018 | null | cs.AI | 20170706 | 20180222 | [
{
"id": "1605.08695"
},
{
"id": "1707.06347"
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{
"id": "1702.08165"
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{
"id": "1704.06440"
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"id": "1509.02971"
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"id": "1606.01540"
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] |
1707.01891 | 41 | Neal Parikh, Stephen Boyd, et al. Proximal algorithms. Foundations and Trends®) in Optimization, 1(3):127-239, 2014.
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Jan Peters, Katharina Mulling, and Yasemin Altun. Relative entropy policy search. In AAAI, 2010.
Konrad Rawlik, Marc Toussaint, and Sethu Vijayakumar. On stochastic optimal control and rein- forcement learning by approximate inference. In Twenty-Third International Joint Conference on Artiï¬cial Intelligence, 2013.
John Schulman. Modular rl. http://github.com/joschu/modular_rl, 2017. Accessed: 2017-06-01.
John Schulman, Sergey Levine, Pieter Abbeel, Michael Jordan, and Philipp Moritz. Trust region policy optimization. In ICML, 2015.
John Schulman, Philipp Moritz, Sergey Levine, Michael Jordan, and Pieter Abbeel. High- dimensional continuous control using generalized advantage estimation. ICLR, 2016.
John Schulman, Pieter Abbeel, and Xi Chen. Equivalence between policy gradients and soft q- learning. arXiv preprint arXiv:1704.06440, 2017a. | 1707.01891#41 | Trust-PCL: An Off-Policy Trust Region Method for Continuous Control | Trust region methods, such as TRPO, are often used to stabilize policy
optimization algorithms in reinforcement learning (RL). While current trust
region strategies are effective for continuous control, they typically require
a prohibitively large amount of on-policy interaction with the environment. To
address this problem, we propose an off-policy trust region method, Trust-PCL.
The algorithm is the result of observing that the optimal policy and state
values of a maximum reward objective with a relative-entropy regularizer
satisfy a set of multi-step pathwise consistencies along any path. Thus,
Trust-PCL is able to maintain optimization stability while exploiting
off-policy data to improve sample efficiency. When evaluated on a number of
continuous control tasks, Trust-PCL improves the solution quality and sample
efficiency of TRPO. | http://arxiv.org/pdf/1707.01891 | Ofir Nachum, Mohammad Norouzi, Kelvin Xu, Dale Schuurmans | cs.AI | ICLR 2018 | null | cs.AI | 20170706 | 20180222 | [
{
"id": "1605.08695"
},
{
"id": "1707.06347"
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"id": "1702.08165"
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"id": "1704.06440"
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"id": "1509.02971"
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"id": "1707.02286"
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1707.01891 | 42 | John Schulman, Filip Wolski, Prafulla Dhariwal, Alec Radford, and Oleg Klimov. Proximal policy optimization algorithms. arXiv preprint arXiv:1707.06347, 2017b.
David Silver, Guy Lever, Nicolas Heess, Thomas Degris, Daan Wierstra, and Martin Riedmiller. Deterministic policy gradient algorithms. In Proceedings of the 31st International Conference on Machine Learning (ICML-14), pp. 387â395, 2014.
Emanuel Todorov, Tom Erez, and Yuval Tassa. Mujoco: A physics engine for model-based control. In Intelligent Robots and Systems (IROS), 2012 IEEE/RSJ International Conference on, pp. 5026â 5033. IEEE, 2012.
Hado Van Hasselt, Arthur Guez, and David Silver. Deep reinforcement learning with double q- learning. AAAI, 2016.
Ziyu Wang, Victor Bapst, Nicolas Heess, Volodymyr Mnih, Remi Munos, Koray Kavukcuoglu, and Nando de Freitas. Sample efï¬cient actor-critic with experience replay. arXiv preprint arXiv:1611.01224, 2016.
Christopher John Cornish Hellaby Watkins. Learning from delayed rewards. PhD thesis, University of Cambridge England, 1989. | 1707.01891#42 | Trust-PCL: An Off-Policy Trust Region Method for Continuous Control | Trust region methods, such as TRPO, are often used to stabilize policy
optimization algorithms in reinforcement learning (RL). While current trust
region strategies are effective for continuous control, they typically require
a prohibitively large amount of on-policy interaction with the environment. To
address this problem, we propose an off-policy trust region method, Trust-PCL.
The algorithm is the result of observing that the optimal policy and state
values of a maximum reward objective with a relative-entropy regularizer
satisfy a set of multi-step pathwise consistencies along any path. Thus,
Trust-PCL is able to maintain optimization stability while exploiting
off-policy data to improve sample efficiency. When evaluated on a number of
continuous control tasks, Trust-PCL improves the solution quality and sample
efficiency of TRPO. | http://arxiv.org/pdf/1707.01891 | Ofir Nachum, Mohammad Norouzi, Kelvin Xu, Dale Schuurmans | cs.AI | ICLR 2018 | null | cs.AI | 20170706 | 20180222 | [
{
"id": "1605.08695"
},
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"id": "1707.06347"
},
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"id": "1702.08165"
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"id": "1704.06440"
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"id": "1509.02971"
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"id": "1707.02286"
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"id": "1611.01224"
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{
"id": "1606.01540"
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{
"id": "1706.00387"
}
] |
1707.01891 | 43 | Christopher John Cornish Hellaby Watkins. Learning from delayed rewards. PhD thesis, University of Cambridge England, 1989.
Ronald J Williams and Jing Peng. Function optimization using connectionist reinforcement learning algorithms. Connection Science, 1991.
11
Published as a conference paper at ICLR 2018
A IMPLEMENTATION BENEFITS OF TRUST-PCL
We have already highlighted the ability of Trust-PCL to use off-policy data to stably train both a parameterized policy and value estimate, which sets it apart from previous methods. We have also noted the ease with which exploration can be incorporated through the entropy regularizer. We elaborate on several additional beneï¬ts of Trust-PCL.
Compared to TRPO, Trust-PCL is much easier to implement. Standard TRPO implementations perform second-order gradient calculations on the KL-divergence to construct a Fisher information matrix (more speciï¬cally a vector product with the inverse Fisher information matrix). This yields a vector direction for which a line search is subsequently employed to ï¬nd the optimal step. Compare this to Trust-PCL which employs simple gradient descent. This makes implementation much more straightforward and easily realizable within standard deep learning frameworks. | 1707.01891#43 | Trust-PCL: An Off-Policy Trust Region Method for Continuous Control | Trust region methods, such as TRPO, are often used to stabilize policy
optimization algorithms in reinforcement learning (RL). While current trust
region strategies are effective for continuous control, they typically require
a prohibitively large amount of on-policy interaction with the environment. To
address this problem, we propose an off-policy trust region method, Trust-PCL.
The algorithm is the result of observing that the optimal policy and state
values of a maximum reward objective with a relative-entropy regularizer
satisfy a set of multi-step pathwise consistencies along any path. Thus,
Trust-PCL is able to maintain optimization stability while exploiting
off-policy data to improve sample efficiency. When evaluated on a number of
continuous control tasks, Trust-PCL improves the solution quality and sample
efficiency of TRPO. | http://arxiv.org/pdf/1707.01891 | Ofir Nachum, Mohammad Norouzi, Kelvin Xu, Dale Schuurmans | cs.AI | ICLR 2018 | null | cs.AI | 20170706 | 20180222 | [
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1707.01891 | 44 | Even if one replaces the constraint on the average KL-divergence of TRPO with a simple regu- larization penalty (as in proximal policy gradient methods (Schulman et al., 2017b; Wang et al., 2016)), optimizing the resulting objective requires computing the gradient of the KL-divergence. In Trust-PCL, there is no such necessity. The per-state KL-divergence need not have an analyt- ically computable gradient. In fact, the KL-divergence need not have a closed form at all. The only requirement of Trust-PCL is that the log-density be analytically computable. This opens up the possible policy parameterizations to a much wider class of functions. While continuous control has traditionally used policies parameterized by unimodal Gaussians, with Trust-PCL the policy can be replaced with something much more expressiveâfor example, mixtures of Gaussians or auto- regressive policies as in Metz et al. (2017).
We have yet to fully explore these additional beneï¬ts in this work, but we hope that future investi- gations can exploit the ï¬exibility and ease of implementation of Trust-PCL to further the progress of RL in continuous control environments.
# B EXPERIMENTAL SETUP
We describe in detail the experimental setup regarding implementation and hyperparameter search. | 1707.01891#44 | Trust-PCL: An Off-Policy Trust Region Method for Continuous Control | Trust region methods, such as TRPO, are often used to stabilize policy
optimization algorithms in reinforcement learning (RL). While current trust
region strategies are effective for continuous control, they typically require
a prohibitively large amount of on-policy interaction with the environment. To
address this problem, we propose an off-policy trust region method, Trust-PCL.
The algorithm is the result of observing that the optimal policy and state
values of a maximum reward objective with a relative-entropy regularizer
satisfy a set of multi-step pathwise consistencies along any path. Thus,
Trust-PCL is able to maintain optimization stability while exploiting
off-policy data to improve sample efficiency. When evaluated on a number of
continuous control tasks, Trust-PCL improves the solution quality and sample
efficiency of TRPO. | http://arxiv.org/pdf/1707.01891 | Ofir Nachum, Mohammad Norouzi, Kelvin Xu, Dale Schuurmans | cs.AI | ICLR 2018 | null | cs.AI | 20170706 | 20180222 | [
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1707.01891 | 45 | # B EXPERIMENTAL SETUP
We describe in detail the experimental setup regarding implementation and hyperparameter search.
# B.1 ENVIRONMENTS
In Acrobot, episodes were cut-off at step 500. For the remaining environments, episodes were cut- off at step 1, 000.
Acrobot, HalfCheetah, and Swimmer are all non-terminating environments. Thus, for these envi- ronments, each episode had equal length and each batch contained the same number of episodes. Hopper, Walker2d, and Ant are environments that can terminate the agent. Thus, for these environ- ments, the batch size throughout training remained constant in terms of steps but not in terms of episodes.
There exists an additional common MuJoCo task called Humanoid. We found that neither our implementation of TRPO nor Trust-PCL could make more than negligible headway on this task, and so omit it from the results. We are aware that TRPO with the addition of GAE and enough ï¬ne- tuning can be made to achieve good results on Humanoid (Schulman et al., 2016). We decided to not pursue a GAE implementation to keep a fair comparison between variants. Trust-PCL can also be made to incorporate an analogue to GAE (by maintaining consistencies at varying time scales), but we leave this to future work.
IMPLEMENTATION DETAILS | 1707.01891#45 | Trust-PCL: An Off-Policy Trust Region Method for Continuous Control | Trust region methods, such as TRPO, are often used to stabilize policy
optimization algorithms in reinforcement learning (RL). While current trust
region strategies are effective for continuous control, they typically require
a prohibitively large amount of on-policy interaction with the environment. To
address this problem, we propose an off-policy trust region method, Trust-PCL.
The algorithm is the result of observing that the optimal policy and state
values of a maximum reward objective with a relative-entropy regularizer
satisfy a set of multi-step pathwise consistencies along any path. Thus,
Trust-PCL is able to maintain optimization stability while exploiting
off-policy data to improve sample efficiency. When evaluated on a number of
continuous control tasks, Trust-PCL improves the solution quality and sample
efficiency of TRPO. | http://arxiv.org/pdf/1707.01891 | Ofir Nachum, Mohammad Norouzi, Kelvin Xu, Dale Schuurmans | cs.AI | ICLR 2018 | null | cs.AI | 20170706 | 20180222 | [
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] |
1707.01891 | 46 | IMPLEMENTATION DETAILS
We use fully-connected feed-forward neural networks to represent both policy and value.
The policy Ïθ is represented by a neural network with two hidden layers of dimension 64 with tanh activations. At time step t, the network is given the observation st. It produces a vector µt, which is combined with a learnable (but t-agnostic) parameter ξ to parametrize a unimodal Gaussian with mean µt and standard deviation exp(ξ). The next action at is sampled randomly from this Gaussian.
12
Published as a conference paper at ICLR 2018
The value network V, is represented by a neural network with two hidden layers of dimension 64 with tanh activations. At time step t the network is given the observation s, and the component-wise squared observation s; © s;. It produces a single scalar value.
# B.2.1 TRPO LEARNING
At each training iteration, both the policy and value parameters are updated. The policy is trained by performing a trust region step according to the procedure described in Schulman et al. (2015). | 1707.01891#46 | Trust-PCL: An Off-Policy Trust Region Method for Continuous Control | Trust region methods, such as TRPO, are often used to stabilize policy
optimization algorithms in reinforcement learning (RL). While current trust
region strategies are effective for continuous control, they typically require
a prohibitively large amount of on-policy interaction with the environment. To
address this problem, we propose an off-policy trust region method, Trust-PCL.
The algorithm is the result of observing that the optimal policy and state
values of a maximum reward objective with a relative-entropy regularizer
satisfy a set of multi-step pathwise consistencies along any path. Thus,
Trust-PCL is able to maintain optimization stability while exploiting
off-policy data to improve sample efficiency. When evaluated on a number of
continuous control tasks, Trust-PCL improves the solution quality and sample
efficiency of TRPO. | http://arxiv.org/pdf/1707.01891 | Ofir Nachum, Mohammad Norouzi, Kelvin Xu, Dale Schuurmans | cs.AI | ICLR 2018 | null | cs.AI | 20170706 | 20180222 | [
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1707.01891 | 47 | At each training iteration, both the policy and value parameters are updated. The policy is trained by performing a trust region step according to the procedure described in Schulman et al. (2015).
The value parameters at each step are solved using an LBFGS optimizer. To avoid instability, the value parameters are solved to fit a mixture of the empirical values and the expected values. That is, we determine ¢ to minimize >, cpacn(Vo(s) â &V3(s) â (1 â %)V3(s))?, where again ¢ is the previous value parameterization. We use & = 0.9. This method for training ¢ is according to that used in|Schulman] (2017).
B.2.2 TRUST-PCL LEARNING
At each training iteration, both the policy and value parameters are updated. The speciï¬c updates are slightly different between Trust-PCL (on-policy) and Trust-PCL (off-policy). | 1707.01891#47 | Trust-PCL: An Off-Policy Trust Region Method for Continuous Control | Trust region methods, such as TRPO, are often used to stabilize policy
optimization algorithms in reinforcement learning (RL). While current trust
region strategies are effective for continuous control, they typically require
a prohibitively large amount of on-policy interaction with the environment. To
address this problem, we propose an off-policy trust region method, Trust-PCL.
The algorithm is the result of observing that the optimal policy and state
values of a maximum reward objective with a relative-entropy regularizer
satisfy a set of multi-step pathwise consistencies along any path. Thus,
Trust-PCL is able to maintain optimization stability while exploiting
off-policy data to improve sample efficiency. When evaluated on a number of
continuous control tasks, Trust-PCL improves the solution quality and sample
efficiency of TRPO. | http://arxiv.org/pdf/1707.01891 | Ofir Nachum, Mohammad Norouzi, Kelvin Xu, Dale Schuurmans | cs.AI | ICLR 2018 | null | cs.AI | 20170706 | 20180222 | [
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1707.01891 | 48 | For Trust-PCL (on-policy), the policy is trained by taking a single gradient step using the Adam optimizer (Kingma & Ba, 2015) with learning rate 0.001. The value network update is inspired by that used in TRPO we perform 5 gradients steps with learning rate 0.001, calculated with regards to a mix between the empirical values and the expected values according to the previous ËÏ. We use κ = 0.95.
For Trust-PCL (off-policy), both the policy and value parameters are updated in a single step using the Adam optimizer with learning rate 0.0001. For this variant, we also utilize a target value network (lagged at the same rate as the target policy network) to replace the value estimate at the ï¬nal state for each path. We do not mix between empirical and expected values.
B.3 HYPERPARAMETER SEARCH | 1707.01891#48 | Trust-PCL: An Off-Policy Trust Region Method for Continuous Control | Trust region methods, such as TRPO, are often used to stabilize policy
optimization algorithms in reinforcement learning (RL). While current trust
region strategies are effective for continuous control, they typically require
a prohibitively large amount of on-policy interaction with the environment. To
address this problem, we propose an off-policy trust region method, Trust-PCL.
The algorithm is the result of observing that the optimal policy and state
values of a maximum reward objective with a relative-entropy regularizer
satisfy a set of multi-step pathwise consistencies along any path. Thus,
Trust-PCL is able to maintain optimization stability while exploiting
off-policy data to improve sample efficiency. When evaluated on a number of
continuous control tasks, Trust-PCL improves the solution quality and sample
efficiency of TRPO. | http://arxiv.org/pdf/1707.01891 | Ofir Nachum, Mohammad Norouzi, Kelvin Xu, Dale Schuurmans | cs.AI | ICLR 2018 | null | cs.AI | 20170706 | 20180222 | [
{
"id": "1605.08695"
},
{
"id": "1707.06347"
},
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"id": "1702.08165"
},
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"id": "1704.06440"
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"id": "1509.02971"
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"id": "1606.01540"
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] |
1707.01891 | 49 | B.3 HYPERPARAMETER SEARCH
We found the most crucial hyperparameters for effective learning in both TRPO and Trust- PCL to be e (the constraint defining the size of the trust region) and d (the rollout determin- ing how to evaluate the empirical value of a state). For TRPO we performed a grid search over ⬠⬠{0.01,0.02,0.05,0.1},d ⬠{10,50}. For Trust-PCL we performed a grid search over ⬠⬠{0.001, 0.002, 0.005, 0.01}, d ⬠{10,50}. For Trust-PCL we also experimented with the value of 7, either keeping it at a constant 0 (thus, no exploration) or decaying it from 0.1 to 0.0 by a smoothed exponential rate of 0.1 every 2,500 training iterations.
We ï¬x the discount to γ = 0.995 for all environments.
# C PSEUDOCODE
A simpliï¬ed pseudocode for Trust-PCL is presented in Algorithm 1.
13
Published as a conference paper at ICLR 2018
# Algorithm 1 Trust-PCL | 1707.01891#49 | Trust-PCL: An Off-Policy Trust Region Method for Continuous Control | Trust region methods, such as TRPO, are often used to stabilize policy
optimization algorithms in reinforcement learning (RL). While current trust
region strategies are effective for continuous control, they typically require
a prohibitively large amount of on-policy interaction with the environment. To
address this problem, we propose an off-policy trust region method, Trust-PCL.
The algorithm is the result of observing that the optimal policy and state
values of a maximum reward objective with a relative-entropy regularizer
satisfy a set of multi-step pathwise consistencies along any path. Thus,
Trust-PCL is able to maintain optimization stability while exploiting
off-policy data to improve sample efficiency. When evaluated on a number of
continuous control tasks, Trust-PCL improves the solution quality and sample
efficiency of TRPO. | http://arxiv.org/pdf/1707.01891 | Ofir Nachum, Mohammad Norouzi, Kelvin Xu, Dale Schuurmans | cs.AI | ICLR 2018 | null | cs.AI | 20170706 | 20180222 | [
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1707.01891 | 51 | function Gradients({sâ S;. ») pte D) 1/C is the consi. stency error sine in Equation|22| P-1 C(g(h , Compute Ad = ye 1Xnso © (s.,. tiptar®s #)VoC(s} hep ttp+ar 99): k , Compute Ad = De 1 Spo cn toe teptar9 8VEC(S tap ta 9, @). Return Ad, Ad end function Initialize 0, 6, A, set 0 = 0. Initialize empty replay buffer RB(). for i = 0 to Nâ1do // Collect Sample P steps si.4p ~ 7 on ENV. Insert s;.44p to RB. // Train Sample batch {s\) t4P B 7 from RB to contain a total of Q transitions (B + Q/P). Aé, Ad = Gradients( ({s\Â¥ tp tbe): Update 6¢ 0â, Ad. Update @ + ¢ â m Ad. // Update auxiliary variables Update 6 = a6 + (1 â a)é. Update in terms of ⬠according to Section[4.3]
# end for
14 | 1707.01891#51 | Trust-PCL: An Off-Policy Trust Region Method for Continuous Control | Trust region methods, such as TRPO, are often used to stabilize policy
optimization algorithms in reinforcement learning (RL). While current trust
region strategies are effective for continuous control, they typically require
a prohibitively large amount of on-policy interaction with the environment. To
address this problem, we propose an off-policy trust region method, Trust-PCL.
The algorithm is the result of observing that the optimal policy and state
values of a maximum reward objective with a relative-entropy regularizer
satisfy a set of multi-step pathwise consistencies along any path. Thus,
Trust-PCL is able to maintain optimization stability while exploiting
off-policy data to improve sample efficiency. When evaluated on a number of
continuous control tasks, Trust-PCL improves the solution quality and sample
efficiency of TRPO. | http://arxiv.org/pdf/1707.01891 | Ofir Nachum, Mohammad Norouzi, Kelvin Xu, Dale Schuurmans | cs.AI | ICLR 2018 | null | cs.AI | 20170706 | 20180222 | [
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"id": "1611.01224"
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"id": "1606.01540"
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"id": "1706.00387"
}
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1707.01495 | 0 | 8 1 0 2
b e F 3 2 ] G L . s c [
3 v 5 9 4 1 0 . 7 0 7 1 : v i X r a
# Hindsight Experience Replay
Marcin Andrychowicz*, Filip Wolski, Alex Ray, Jonas Schneider, Rachel Fong, Peter Welinder, Bob McGrew, Josh Tobin, Pieter Abbeel', Wojciech Zarembaâ OpenAI
# Abstract
Dealing with sparse rewards is one of the biggest challenges in Reinforcement Learning (RL). We present a novel technique called Hindsight Experience Replay which allows sample-efficient learning from rewards which are sparse and binary and therefore avoid the need for complicated reward engineering. It can be com- bined with an arbitrary off-policy RL algorithm and may be seen as a form of implicit curriculum.
We demonstrate our approach on the task of manipulating objects with a robotic arm. In particular, we run experiments on three different tasks: pushing, sliding, and pick-and-place, in each case using only binary rewards indicating whether or not the task is completed. Our ablation studies show that Hindsight Experience Replay is a crucial ingredient which makes training possible in these challenging environments. We show that our policies trained on a physics simulation can be deployed on a physical robot and successfully complete the task. The video presenting our experiments is available at https: //goo.gl1/SMrQnI.
# 1 Introduction | 1707.01495#0 | Hindsight Experience Replay | Dealing with sparse rewards is one of the biggest challenges in Reinforcement
Learning (RL). We present a novel technique called Hindsight Experience Replay
which allows sample-efficient learning from rewards which are sparse and binary
and therefore avoid the need for complicated reward engineering. It can be
combined with an arbitrary off-policy RL algorithm and may be seen as a form of
implicit curriculum.
We demonstrate our approach on the task of manipulating objects with a
robotic arm. In particular, we run experiments on three different tasks:
pushing, sliding, and pick-and-place, in each case using only binary rewards
indicating whether or not the task is completed. Our ablation studies show that
Hindsight Experience Replay is a crucial ingredient which makes training
possible in these challenging environments. We show that our policies trained
on a physics simulation can be deployed on a physical robot and successfully
complete the task. | http://arxiv.org/pdf/1707.01495 | Marcin Andrychowicz, Filip Wolski, Alex Ray, Jonas Schneider, Rachel Fong, Peter Welinder, Bob McGrew, Josh Tobin, Pieter Abbeel, Wojciech Zaremba | cs.LG, cs.AI, cs.NE, cs.RO | null | null | cs.LG | 20170705 | 20180223 | [
{
"id": "1511.05952"
},
{
"id": "1611.04717"
},
{
"id": "1703.06907"
},
{
"id": "1509.02971"
}
] |
1707.01495 | 1 | # 1 Introduction
Reinforcement learning (RL) combined with neural networks has recently led to a wide range of successes in learning policies for sequential decision-making problems. This includes simulated environments, such as playing Atari games (Mnih et al., 2015), and defeating the best human player at the game of Go (Silver et al., 2016), as well as robotic tasks such as helicopter control (Ng et al., 2006), hitting a baseball (Peters and Schaal, 2008), screwing a cap onto a bottle (Levine et al., 2015), or door opening (Chebotar et al., 2016).
However, a common challenge, especially for robotics, is the need to engineer a reward function that not only reflects the task at hand but is also carefully shaped (Ng et al., 1999) to guide the policy optimization. For example, Popov et al. (2017) use a cost function consisting of five relatively complicated terms which need to be carefully weighted in order to train a policy for stacking a brick on top of another one. The necessity of cost engineering limits the applicability of RL in the real world because it requires both RL expertise and domain-specific knowledge. Moreover, it is not applicable in situations where we do not know what admissible behaviour may look like. It is therefore of great practical relevance to develop algorithms which can learn from unshaped reward signals, e.g. a binary signal indicating successful task completion. | 1707.01495#1 | Hindsight Experience Replay | Dealing with sparse rewards is one of the biggest challenges in Reinforcement
Learning (RL). We present a novel technique called Hindsight Experience Replay
which allows sample-efficient learning from rewards which are sparse and binary
and therefore avoid the need for complicated reward engineering. It can be
combined with an arbitrary off-policy RL algorithm and may be seen as a form of
implicit curriculum.
We demonstrate our approach on the task of manipulating objects with a
robotic arm. In particular, we run experiments on three different tasks:
pushing, sliding, and pick-and-place, in each case using only binary rewards
indicating whether or not the task is completed. Our ablation studies show that
Hindsight Experience Replay is a crucial ingredient which makes training
possible in these challenging environments. We show that our policies trained
on a physics simulation can be deployed on a physical robot and successfully
complete the task. | http://arxiv.org/pdf/1707.01495 | Marcin Andrychowicz, Filip Wolski, Alex Ray, Jonas Schneider, Rachel Fong, Peter Welinder, Bob McGrew, Josh Tobin, Pieter Abbeel, Wojciech Zaremba | cs.LG, cs.AI, cs.NE, cs.RO | null | null | cs.LG | 20170705 | 20180223 | [
{
"id": "1511.05952"
},
{
"id": "1611.04717"
},
{
"id": "1703.06907"
},
{
"id": "1509.02971"
}
] |
1707.01495 | 2 | One ability humans have, unlike the current generation of model-free RL algorithms, is to learn almost as much from achieving an undesired outcome as from the desired one. Imagine that you are learning how to play hockey and are trying to shoot a puck into a net. You hit the puck but it misses the net on the right side. The conclusion drawn by a standard RL algorithm in such a situation would
*
[email protected] t
Equal advising.
31st Conference on Neural Information Processing Systems (NIPS 2017), Long Beach, CA, USA.
be that the performed sequence of actions does not lead to a successful shot, and little (if anything) would be learned. It is however possible to draw another conclusion, namely that this sequence of actions would be successful if the net had been placed further to the right. | 1707.01495#2 | Hindsight Experience Replay | Dealing with sparse rewards is one of the biggest challenges in Reinforcement
Learning (RL). We present a novel technique called Hindsight Experience Replay
which allows sample-efficient learning from rewards which are sparse and binary
and therefore avoid the need for complicated reward engineering. It can be
combined with an arbitrary off-policy RL algorithm and may be seen as a form of
implicit curriculum.
We demonstrate our approach on the task of manipulating objects with a
robotic arm. In particular, we run experiments on three different tasks:
pushing, sliding, and pick-and-place, in each case using only binary rewards
indicating whether or not the task is completed. Our ablation studies show that
Hindsight Experience Replay is a crucial ingredient which makes training
possible in these challenging environments. We show that our policies trained
on a physics simulation can be deployed on a physical robot and successfully
complete the task. | http://arxiv.org/pdf/1707.01495 | Marcin Andrychowicz, Filip Wolski, Alex Ray, Jonas Schneider, Rachel Fong, Peter Welinder, Bob McGrew, Josh Tobin, Pieter Abbeel, Wojciech Zaremba | cs.LG, cs.AI, cs.NE, cs.RO | null | null | cs.LG | 20170705 | 20180223 | [
{
"id": "1511.05952"
},
{
"id": "1611.04717"
},
{
"id": "1703.06907"
},
{
"id": "1509.02971"
}
] |
1707.01495 | 3 | In this paper we introduce a technique called Hindsight Experience Replay (HER) which allows the algorithm to perform exactly this kind of reasoning and can be combined with any off-policy RL algorithm. It is applicable whenever there are multiple goals which can be achieved, e.g. achieving each state of the system may be treated as a separate goal. Not only does HER improve the sample efficiency in this setting, but more importantly, it makes learning possible even if the reward signal is sparse and binary. Our approach is based on training universal policies (Schaul et al., 2015a) which take as input not only the current state, but also a goal state. The pivotal idea behind HER is to replay each episode with a different goal than the one the agent was trying to achieve, e.g. one of the goals which was achieved in the episode.
# 2 Background
In this section we introduce reinforcement learning formalism used in the paper as well as RL algorithms we use in our experiments.
# 2.1 Reinforcement Learning
We consider the standard reinforcement learning formalism consisting of an agent interacting with an environment. To simplify the exposition we assume that the environment is fully observable. An environment is described by a set of states S, a set of actions A, a distribution of initial states p(so), a reward function r : S x A â R, transition probabilities p(s:41|s¢, a), and a discount factor 7 ⬠[0,1]. | 1707.01495#3 | Hindsight Experience Replay | Dealing with sparse rewards is one of the biggest challenges in Reinforcement
Learning (RL). We present a novel technique called Hindsight Experience Replay
which allows sample-efficient learning from rewards which are sparse and binary
and therefore avoid the need for complicated reward engineering. It can be
combined with an arbitrary off-policy RL algorithm and may be seen as a form of
implicit curriculum.
We demonstrate our approach on the task of manipulating objects with a
robotic arm. In particular, we run experiments on three different tasks:
pushing, sliding, and pick-and-place, in each case using only binary rewards
indicating whether or not the task is completed. Our ablation studies show that
Hindsight Experience Replay is a crucial ingredient which makes training
possible in these challenging environments. We show that our policies trained
on a physics simulation can be deployed on a physical robot and successfully
complete the task. | http://arxiv.org/pdf/1707.01495 | Marcin Andrychowicz, Filip Wolski, Alex Ray, Jonas Schneider, Rachel Fong, Peter Welinder, Bob McGrew, Josh Tobin, Pieter Abbeel, Wojciech Zaremba | cs.LG, cs.AI, cs.NE, cs.RO | null | null | cs.LG | 20170705 | 20180223 | [
{
"id": "1511.05952"
},
{
"id": "1611.04717"
},
{
"id": "1703.06907"
},
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"id": "1509.02971"
}
] |
1707.01495 | 4 | A deterministic policy is a mapping from states to actions: 7 : S â A. Every episode starts with sampling an initial state s9. At every timestep ¢ the agent produces an action based on the current state: ay = 7(8,). Then it gets the reward r; = r(sz, a) and the environmentâs new state is sampled from the distribution p(-|s;, a). A discounted sum of future rewards is called a return: Ry = y=, yi. The agentâs goal is to maximize its expected return E,,,[Ro|so]. The Q-function or action-value function is defined as Qâ(s;, ar) = E[R;|s¢, ai].
Let * denote an optimal policy i.e. any policy 1* s.t. Q⢠(s, a) > Q7(s,a) for every s ⬠S,ae A and any policy 7. All optimal policies have the same Q-function which is called optimal Q-function and denoted Q*. It is easy to show that it satisfies the following equation called the Bellman equation:
Q"(s.4) = Exep¢jsa) [r(ssa) + ymax Q*(s',a!)|
# 2.2 Deep Q-Networks (DQN) | 1707.01495#4 | Hindsight Experience Replay | Dealing with sparse rewards is one of the biggest challenges in Reinforcement
Learning (RL). We present a novel technique called Hindsight Experience Replay
which allows sample-efficient learning from rewards which are sparse and binary
and therefore avoid the need for complicated reward engineering. It can be
combined with an arbitrary off-policy RL algorithm and may be seen as a form of
implicit curriculum.
We demonstrate our approach on the task of manipulating objects with a
robotic arm. In particular, we run experiments on three different tasks:
pushing, sliding, and pick-and-place, in each case using only binary rewards
indicating whether or not the task is completed. Our ablation studies show that
Hindsight Experience Replay is a crucial ingredient which makes training
possible in these challenging environments. We show that our policies trained
on a physics simulation can be deployed on a physical robot and successfully
complete the task. | http://arxiv.org/pdf/1707.01495 | Marcin Andrychowicz, Filip Wolski, Alex Ray, Jonas Schneider, Rachel Fong, Peter Welinder, Bob McGrew, Josh Tobin, Pieter Abbeel, Wojciech Zaremba | cs.LG, cs.AI, cs.NE, cs.RO | null | null | cs.LG | 20170705 | 20180223 | [
{
"id": "1511.05952"
},
{
"id": "1611.04717"
},
{
"id": "1703.06907"
},
{
"id": "1509.02971"
}
] |
1707.01495 | 5 | # 2.2 Deep Q-Networks (DQN)
Deep Q-Networks (DQN) (Mnih et al., 2015) is a model-free RL algorithm for discrete action spaces. Here we sketch it only informally, see Mnih et al. (2015) for more details. In DQN we maintain a neural network Q which approximates Q*. A greedy policy w.r.t. Q is defined as T@Q(s) = argmax,¢ ,Q(s, a). An â¬-greedy policy w.r.t. Q is a policy which with probability ⬠takes a random action (sampled uniformly from A) and takes the action 7g(s) with probability 1 â «. | 1707.01495#5 | Hindsight Experience Replay | Dealing with sparse rewards is one of the biggest challenges in Reinforcement
Learning (RL). We present a novel technique called Hindsight Experience Replay
which allows sample-efficient learning from rewards which are sparse and binary
and therefore avoid the need for complicated reward engineering. It can be
combined with an arbitrary off-policy RL algorithm and may be seen as a form of
implicit curriculum.
We demonstrate our approach on the task of manipulating objects with a
robotic arm. In particular, we run experiments on three different tasks:
pushing, sliding, and pick-and-place, in each case using only binary rewards
indicating whether or not the task is completed. Our ablation studies show that
Hindsight Experience Replay is a crucial ingredient which makes training
possible in these challenging environments. We show that our policies trained
on a physics simulation can be deployed on a physical robot and successfully
complete the task. | http://arxiv.org/pdf/1707.01495 | Marcin Andrychowicz, Filip Wolski, Alex Ray, Jonas Schneider, Rachel Fong, Peter Welinder, Bob McGrew, Josh Tobin, Pieter Abbeel, Wojciech Zaremba | cs.LG, cs.AI, cs.NE, cs.RO | null | null | cs.LG | 20170705 | 20180223 | [
{
"id": "1511.05952"
},
{
"id": "1611.04717"
},
{
"id": "1703.06907"
},
{
"id": "1509.02971"
}
] |
1707.01495 | 6 | During training we generate episodes using e-greedy policy w.r.t. the current approximation of the action-value function Q. The transition tuples (s;, a¢, 4, $41) encountered during training are stored in the so-called replay buffer. The generation of new episodes is interleaved with neural network training. The network is trained using mini-batch gradient descent on the loss £ which encourages the approximated Q-function to satisfy the Bellman equation: £ = E (Q(s:, az) â yt). where yz = ry + YMaxec.4 Q(sy41, aâ) and the tuples (51, a4, rz, 8¢41) are sampled from the replay buffer'.
In order to make this optimization procedure more stable the targets y, are usually computed using a separate target network which changes at a slower pace than the main network. A common practice
'The targets y, depend on the network parameters but this dependency is ignored during backpropagation.
is to periodically set the weights of the target network to the current weights of the main network (e.g. Mnih et al. (2015)) or to use a polyak-averagedâ (Polyak and Juditsky, 1992) version of the main network instead (Lillicrap et al., 2015).
# 2.3 Deep Deterministic Policy Gradients (DDPG) | 1707.01495#6 | Hindsight Experience Replay | Dealing with sparse rewards is one of the biggest challenges in Reinforcement
Learning (RL). We present a novel technique called Hindsight Experience Replay
which allows sample-efficient learning from rewards which are sparse and binary
and therefore avoid the need for complicated reward engineering. It can be
combined with an arbitrary off-policy RL algorithm and may be seen as a form of
implicit curriculum.
We demonstrate our approach on the task of manipulating objects with a
robotic arm. In particular, we run experiments on three different tasks:
pushing, sliding, and pick-and-place, in each case using only binary rewards
indicating whether or not the task is completed. Our ablation studies show that
Hindsight Experience Replay is a crucial ingredient which makes training
possible in these challenging environments. We show that our policies trained
on a physics simulation can be deployed on a physical robot and successfully
complete the task. | http://arxiv.org/pdf/1707.01495 | Marcin Andrychowicz, Filip Wolski, Alex Ray, Jonas Schneider, Rachel Fong, Peter Welinder, Bob McGrew, Josh Tobin, Pieter Abbeel, Wojciech Zaremba | cs.LG, cs.AI, cs.NE, cs.RO | null | null | cs.LG | 20170705 | 20180223 | [
{
"id": "1511.05952"
},
{
"id": "1611.04717"
},
{
"id": "1703.06907"
},
{
"id": "1509.02971"
}
] |
1707.01495 | 7 | # 2.3 Deep Deterministic Policy Gradients (DDPG)
Deep Deterministic Policy Gradients (DDPG) (Lillicrap et al., 2015) is a model-free RL algorithm for continuous action spaces. Here we sketch it only informally, see Lillicrap et al. (2015) for more details. In DDPG we maintain two neural networks: a target policy (also called an actor) 7: S > A and an action-value function approximator (called the critic) Q : S x A â R. The criticâs job is to approximate the actorâs action-value function Qâ.
Episodes are generated using a behavioral policy which is a noisy version of the target policy, e.g. mâ¢(s) = 1(s) + N(0,1). The critic is trained in a similar way as the Q-function in DQN but the targets y, are computed using actions outputted by the actor, ie. y, = ry + YQ(S141,7(St41))- The actor is trained with mini-batch gradient descent on the loss £, = âE,Q(s,7(s)), where s is sampled from the replay buffer. The gradient of £, w.r.t. actor parameters can be computed by backpropagation through the combined critic and actor networks. | 1707.01495#7 | Hindsight Experience Replay | Dealing with sparse rewards is one of the biggest challenges in Reinforcement
Learning (RL). We present a novel technique called Hindsight Experience Replay
which allows sample-efficient learning from rewards which are sparse and binary
and therefore avoid the need for complicated reward engineering. It can be
combined with an arbitrary off-policy RL algorithm and may be seen as a form of
implicit curriculum.
We demonstrate our approach on the task of manipulating objects with a
robotic arm. In particular, we run experiments on three different tasks:
pushing, sliding, and pick-and-place, in each case using only binary rewards
indicating whether or not the task is completed. Our ablation studies show that
Hindsight Experience Replay is a crucial ingredient which makes training
possible in these challenging environments. We show that our policies trained
on a physics simulation can be deployed on a physical robot and successfully
complete the task. | http://arxiv.org/pdf/1707.01495 | Marcin Andrychowicz, Filip Wolski, Alex Ray, Jonas Schneider, Rachel Fong, Peter Welinder, Bob McGrew, Josh Tobin, Pieter Abbeel, Wojciech Zaremba | cs.LG, cs.AI, cs.NE, cs.RO | null | null | cs.LG | 20170705 | 20180223 | [
{
"id": "1511.05952"
},
{
"id": "1611.04717"
},
{
"id": "1703.06907"
},
{
"id": "1509.02971"
}
] |
1707.01495 | 8 | # 2.4 Universal Value Function Approximators (UVFA)
Universal Value Function Approximators (UVFA) (Schaul et al., 2015a) is an extension of DQN to the setup where there is more than one goal we may try to achieve. Let G be the space of possible goals. Every goal g ⬠G corresponds to some reward function rz : S x A â R. Every episode starts with sampling a state-goal pair from some distribution p(so, g). The goal stays fixed for the whole episode. At every timestep the agent gets as input not only the current state but also the current goal a:SxG-â Aand gets the reward r, = r,(s;,a;,). The Q-function now depends not only on a state-action pair but also on a goal Q*(s;, a1, 9) = E[R:|s:, at, g]. Schaul et al. (2015a) show that in this setup it is possible to train an approximator to the Q-function using direct bootstrapping from the Bellman equation (just like in case of DQN) and that a greedy policy derived from it can generalize to previously unseen state-action pairs. The extension of this approach to DDPG is straightforward.
# 3 Hindsight Experience Replay
# 3.1 A motivating example | 1707.01495#8 | Hindsight Experience Replay | Dealing with sparse rewards is one of the biggest challenges in Reinforcement
Learning (RL). We present a novel technique called Hindsight Experience Replay
which allows sample-efficient learning from rewards which are sparse and binary
and therefore avoid the need for complicated reward engineering. It can be
combined with an arbitrary off-policy RL algorithm and may be seen as a form of
implicit curriculum.
We demonstrate our approach on the task of manipulating objects with a
robotic arm. In particular, we run experiments on three different tasks:
pushing, sliding, and pick-and-place, in each case using only binary rewards
indicating whether or not the task is completed. Our ablation studies show that
Hindsight Experience Replay is a crucial ingredient which makes training
possible in these challenging environments. We show that our policies trained
on a physics simulation can be deployed on a physical robot and successfully
complete the task. | http://arxiv.org/pdf/1707.01495 | Marcin Andrychowicz, Filip Wolski, Alex Ray, Jonas Schneider, Rachel Fong, Peter Welinder, Bob McGrew, Josh Tobin, Pieter Abbeel, Wojciech Zaremba | cs.LG, cs.AI, cs.NE, cs.RO | null | null | cs.LG | 20170705 | 20180223 | [
{
"id": "1511.05952"
},
{
"id": "1611.04717"
},
{
"id": "1703.06907"
},
{
"id": "1509.02971"
}
] |
1707.01495 | 9 | # 3 Hindsight Experience Replay
# 3.1 A motivating example
Consider a bit-flipping environment with the state space S = {0, 1}â and the action space A = {0,1,..., â 1} for some integer n in which executing the i-th action flips the i-th bit of the state. For every episode we sample uniformly an initial state as well as a target state and the policy gets a reward of â1 as long as it is not in the target state, i.e. rg(s,a) = â[s F g]. | 1707.01495#9 | Hindsight Experience Replay | Dealing with sparse rewards is one of the biggest challenges in Reinforcement
Learning (RL). We present a novel technique called Hindsight Experience Replay
which allows sample-efficient learning from rewards which are sparse and binary
and therefore avoid the need for complicated reward engineering. It can be
combined with an arbitrary off-policy RL algorithm and may be seen as a form of
implicit curriculum.
We demonstrate our approach on the task of manipulating objects with a
robotic arm. In particular, we run experiments on three different tasks:
pushing, sliding, and pick-and-place, in each case using only binary rewards
indicating whether or not the task is completed. Our ablation studies show that
Hindsight Experience Replay is a crucial ingredient which makes training
possible in these challenging environments. We show that our policies trained
on a physics simulation can be deployed on a physical robot and successfully
complete the task. | http://arxiv.org/pdf/1707.01495 | Marcin Andrychowicz, Filip Wolski, Alex Ray, Jonas Schneider, Rachel Fong, Peter Welinder, Bob McGrew, Josh Tobin, Pieter Abbeel, Wojciech Zaremba | cs.LG, cs.AI, cs.NE, cs.RO | null | null | cs.LG | 20170705 | 20180223 | [
{
"id": "1511.05952"
},
{
"id": "1611.04717"
},
{
"id": "1703.06907"
},
{
"id": "1509.02971"
}
] |
1707.01495 | 10 | Standard RL algorithms are bound to fail in this environment for n > 40 because they will never experience any reward other than â1. Figure Notice that using techniques for improving exploration (e.g. VIME ment. (Houthooft et al., 2016), count-based exploration (Ostrovski et al., 2017) or bootstrapped DQN (Osband et al., 2016)) does not help here because the real problem is not in lack of diversity of states being visited, rather it is simply impractical to explore such a large state space. The standard solution to this problem would be to use 08 a shaped reward function which is more informative and guides the agent towards the goal, e.g. ry(s,a@) = â||s â g||°. While using a shaped reward solves the problem in our toy environment, it may be difficult to apply to more complicated problems. We investigate the results of reward shaping experimentally in Sec. 4.4. 0.6 0.4 success rate ° =
Instead of shaping the reward we propose a different solution which does not require any domain knowledge. Consider an episode with
Figure 1: Bit-flipping experi- ment.
== DON â DQN+HER 08 0.6 0.4 success rate ° = iy o 2 ° 10 20 30 40 50 number of bits n ° | 1707.01495#10 | Hindsight Experience Replay | Dealing with sparse rewards is one of the biggest challenges in Reinforcement
Learning (RL). We present a novel technique called Hindsight Experience Replay
which allows sample-efficient learning from rewards which are sparse and binary
and therefore avoid the need for complicated reward engineering. It can be
combined with an arbitrary off-policy RL algorithm and may be seen as a form of
implicit curriculum.
We demonstrate our approach on the task of manipulating objects with a
robotic arm. In particular, we run experiments on three different tasks:
pushing, sliding, and pick-and-place, in each case using only binary rewards
indicating whether or not the task is completed. Our ablation studies show that
Hindsight Experience Replay is a crucial ingredient which makes training
possible in these challenging environments. We show that our policies trained
on a physics simulation can be deployed on a physical robot and successfully
complete the task. | http://arxiv.org/pdf/1707.01495 | Marcin Andrychowicz, Filip Wolski, Alex Ray, Jonas Schneider, Rachel Fong, Peter Welinder, Bob McGrew, Josh Tobin, Pieter Abbeel, Wojciech Zaremba | cs.LG, cs.AI, cs.NE, cs.RO | null | null | cs.LG | 20170705 | 20180223 | [
{
"id": "1511.05952"
},
{
"id": "1611.04717"
},
{
"id": "1703.06907"
},
{
"id": "1509.02971"
}
] |
1707.01495 | 12 | a state sequence s),..., 57 anda goal g 4 s1,..., 87 which implies
that the agent received a reward of â1 at every timestep. The pivotal idea behind our approach is to re-examine this trajectory with a different goal â while this trajectory may not help us learn how to achieve the state g, it definitely tells us something about how to achieve the state s;. This information can be harvested by using an off-policy RL algorithm and experience replay where we replace g in the replay buffer by sp. In addition we can still replay with the original goal g left intact in the replay buffer. With this modification at least half of the replayed trajectories contain rewards different from â1 and learning becomes much simpler. Fig. 1 compares the final performance of DQN with and without this additional replay technique which we call Hindsight Experience Replay (HER). DQN without HER can only solve the task for n < 13 while DQN with HER easily solves the task for n up to 50. See Appendix A for the details of the experimental setup. Note that this approach combined with powerful function approximators (e.g., deep neural networks) allows the agent to learn how to achieve the goal g even if it has never observed it during training.
We more formally describe our approach in the following sections.
# 3.2. Multi-goal RL | 1707.01495#12 | Hindsight Experience Replay | Dealing with sparse rewards is one of the biggest challenges in Reinforcement
Learning (RL). We present a novel technique called Hindsight Experience Replay
which allows sample-efficient learning from rewards which are sparse and binary
and therefore avoid the need for complicated reward engineering. It can be
combined with an arbitrary off-policy RL algorithm and may be seen as a form of
implicit curriculum.
We demonstrate our approach on the task of manipulating objects with a
robotic arm. In particular, we run experiments on three different tasks:
pushing, sliding, and pick-and-place, in each case using only binary rewards
indicating whether or not the task is completed. Our ablation studies show that
Hindsight Experience Replay is a crucial ingredient which makes training
possible in these challenging environments. We show that our policies trained
on a physics simulation can be deployed on a physical robot and successfully
complete the task. | http://arxiv.org/pdf/1707.01495 | Marcin Andrychowicz, Filip Wolski, Alex Ray, Jonas Schneider, Rachel Fong, Peter Welinder, Bob McGrew, Josh Tobin, Pieter Abbeel, Wojciech Zaremba | cs.LG, cs.AI, cs.NE, cs.RO | null | null | cs.LG | 20170705 | 20180223 | [
{
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},
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"id": "1611.04717"
},
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"id": "1703.06907"
},
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"id": "1509.02971"
}
] |
1707.01495 | 13 | We more formally describe our approach in the following sections.
# 3.2. Multi-goal RL
We are interested in training agents which learn to achieve multiple different goals. We follow the approach from Universal Value Function Approximators (Schaul et al., 2015a), i.e. we train policies and value functions which take as input not only a state s ⬠S but also a goal g ⬠G. Moreover, we show that training an agent to perform multiple tasks can be easier than training it to perform only one task (see Sec. 4.3 for details) and therefore our approach may be applicable even if there is only one task we would like the agent to perform (a similar situation was recently observed by Pinto and Gupta (2016)).
We assume that every goal g ⬠G corresponds to some predicate f, : S â {0,1} and that the agentâs goal is to achieve any state s that satisfies f,(s) = 1. In the case when we want to exactly specify the desired state of the system we may use S = G and f,(s) = [s = g]. The goals can also specify only some properties of the state, e.g. suppose that S = R? and we want to be able to achieve an arbitrary state with the given value of x coordinate. In this case G = R and f,((x,y)) = [x = g]. | 1707.01495#13 | Hindsight Experience Replay | Dealing with sparse rewards is one of the biggest challenges in Reinforcement
Learning (RL). We present a novel technique called Hindsight Experience Replay
which allows sample-efficient learning from rewards which are sparse and binary
and therefore avoid the need for complicated reward engineering. It can be
combined with an arbitrary off-policy RL algorithm and may be seen as a form of
implicit curriculum.
We demonstrate our approach on the task of manipulating objects with a
robotic arm. In particular, we run experiments on three different tasks:
pushing, sliding, and pick-and-place, in each case using only binary rewards
indicating whether or not the task is completed. Our ablation studies show that
Hindsight Experience Replay is a crucial ingredient which makes training
possible in these challenging environments. We show that our policies trained
on a physics simulation can be deployed on a physical robot and successfully
complete the task. | http://arxiv.org/pdf/1707.01495 | Marcin Andrychowicz, Filip Wolski, Alex Ray, Jonas Schneider, Rachel Fong, Peter Welinder, Bob McGrew, Josh Tobin, Pieter Abbeel, Wojciech Zaremba | cs.LG, cs.AI, cs.NE, cs.RO | null | null | cs.LG | 20170705 | 20180223 | [
{
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},
{
"id": "1611.04717"
},
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"id": "1703.06907"
},
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"id": "1509.02971"
}
] |
1707.01495 | 14 | Moreover, we assume that given a state s we can easily find a goal g which is satisfied in this state. More formally, we assume that there is given a mapping m : S > G s.t. Vses fm(s)(s) = 1. Notice that this assumption is not very restrictive and can usually be satisfied. In the case where each goal corresponds to a state we want to achieve, ie. G = S and f(s) = [s = g], the mapping m is just an identity. For the case of 2-dimensional state and 1-dimensional goals from the previous paragraph this mapping is also very simple m((x,y)) = 2.
A universal policy can be trained using an arbitrary RL algorithm by sampling goals and initial states from some distributions, running the agent for some number of timesteps and giving it a negative reward at every timestep when the goal is not achieved, i.e. rg(s,a) = â[fy(s) = 0]. This does not however work very well in practice because this reward function is sparse and not very informative.
In order to solve this problem we introduce the technique of Hindsight Experience Replay which is the crux of our approach.
# 3.3 Algorithm | 1707.01495#14 | Hindsight Experience Replay | Dealing with sparse rewards is one of the biggest challenges in Reinforcement
Learning (RL). We present a novel technique called Hindsight Experience Replay
which allows sample-efficient learning from rewards which are sparse and binary
and therefore avoid the need for complicated reward engineering. It can be
combined with an arbitrary off-policy RL algorithm and may be seen as a form of
implicit curriculum.
We demonstrate our approach on the task of manipulating objects with a
robotic arm. In particular, we run experiments on three different tasks:
pushing, sliding, and pick-and-place, in each case using only binary rewards
indicating whether or not the task is completed. Our ablation studies show that
Hindsight Experience Replay is a crucial ingredient which makes training
possible in these challenging environments. We show that our policies trained
on a physics simulation can be deployed on a physical robot and successfully
complete the task. | http://arxiv.org/pdf/1707.01495 | Marcin Andrychowicz, Filip Wolski, Alex Ray, Jonas Schneider, Rachel Fong, Peter Welinder, Bob McGrew, Josh Tobin, Pieter Abbeel, Wojciech Zaremba | cs.LG, cs.AI, cs.NE, cs.RO | null | null | cs.LG | 20170705 | 20180223 | [
{
"id": "1511.05952"
},
{
"id": "1611.04717"
},
{
"id": "1703.06907"
},
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"id": "1509.02971"
}
] |
1707.01495 | 15 | In order to solve this problem we introduce the technique of Hindsight Experience Replay which is the crux of our approach.
# 3.3 Algorithm
The idea behind Hindsight Experience Replay (HER) is very simple: after experiencing some episode So, S1,.--, 87 We Store in the replay buffer every transition s; â s;, not only with the original goal used for this episode but also with a subset of other goals. Notice that the goal being pursued influences the agentâs actions but not the environment dynamics and therefore we can replay each trajectory with an arbitrary goal assuming that we use an off-policy RL algorithm like DQN (Mnih et al., 2015), DDPG (Lillicrap et al., 2015), NAF (Gu et al., 2016) or SDQN (Metz et al., 2017).
One choice which has to be made in order to use HER is the set of additional goals used for replay. In the simplest version of our algorithm we replay each trajectory with the goal m(sr), i.e. the goal which is achieved in the final state of the episode. We experimentally compare different types and quantities of additional goals for replay in Sec. 4.5. In all cases we also replay each trajectory with the original goal pursued in the episode. See Alg. 1 for a more formal description of the algorithm.
Algorithm 1 Hindsight Experience Replay (HER)
# Given: | 1707.01495#15 | Hindsight Experience Replay | Dealing with sparse rewards is one of the biggest challenges in Reinforcement
Learning (RL). We present a novel technique called Hindsight Experience Replay
which allows sample-efficient learning from rewards which are sparse and binary
and therefore avoid the need for complicated reward engineering. It can be
combined with an arbitrary off-policy RL algorithm and may be seen as a form of
implicit curriculum.
We demonstrate our approach on the task of manipulating objects with a
robotic arm. In particular, we run experiments on three different tasks:
pushing, sliding, and pick-and-place, in each case using only binary rewards
indicating whether or not the task is completed. Our ablation studies show that
Hindsight Experience Replay is a crucial ingredient which makes training
possible in these challenging environments. We show that our policies trained
on a physics simulation can be deployed on a physical robot and successfully
complete the task. | http://arxiv.org/pdf/1707.01495 | Marcin Andrychowicz, Filip Wolski, Alex Ray, Jonas Schneider, Rachel Fong, Peter Welinder, Bob McGrew, Josh Tobin, Pieter Abbeel, Wojciech Zaremba | cs.LG, cs.AI, cs.NE, cs.RO | null | null | cs.LG | 20170705 | 20180223 | [
{
"id": "1511.05952"
},
{
"id": "1611.04717"
},
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"id": "1703.06907"
},
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"id": "1509.02971"
}
] |
1707.01495 | 17 | an off-policy RL algorithm A, > e.g. DQN, DDPG, NAF, SDQN astrategy S for sampling goals for replay, peg. S(so,---, 87) = m(sr) areward functionr: Sx AxGâ>R. peg. r(s,a,9) = â[fg(s) = 0] Initialize A > e.g. initialize neural networks Initialize replay buffer R episode =1, / do Sample a goal g and an initial state so. fort = 0,Tâ1do Sample an action a; using the behavioral policy from A: ar â 7(S:|[g) > || denotes concatenation Execute the action a; and observe a new state s;41 end for fort = 0,Tâ1do re = 1 (St, Gt, 9) Store the transition (s;||g, az, Te, $¢41||g) in R > standard experience replay Sample a set of additional goals for replay G := S(current episode) for g' ⬠Gdo râ := 7(81, 41,9â) Store the transition (s;||gâ, ae, 7â, Se41||gâ) in R > HER end | 1707.01495#17 | Hindsight Experience Replay | Dealing with sparse rewards is one of the biggest challenges in Reinforcement
Learning (RL). We present a novel technique called Hindsight Experience Replay
which allows sample-efficient learning from rewards which are sparse and binary
and therefore avoid the need for complicated reward engineering. It can be
combined with an arbitrary off-policy RL algorithm and may be seen as a form of
implicit curriculum.
We demonstrate our approach on the task of manipulating objects with a
robotic arm. In particular, we run experiments on three different tasks:
pushing, sliding, and pick-and-place, in each case using only binary rewards
indicating whether or not the task is completed. Our ablation studies show that
Hindsight Experience Replay is a crucial ingredient which makes training
possible in these challenging environments. We show that our policies trained
on a physics simulation can be deployed on a physical robot and successfully
complete the task. | http://arxiv.org/pdf/1707.01495 | Marcin Andrychowicz, Filip Wolski, Alex Ray, Jonas Schneider, Rachel Fong, Peter Welinder, Bob McGrew, Josh Tobin, Pieter Abbeel, Wojciech Zaremba | cs.LG, cs.AI, cs.NE, cs.RO | null | null | cs.LG | 20170705 | 20180223 | [
{
"id": "1511.05952"
},
{
"id": "1611.04717"
},
{
"id": "1703.06907"
},
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}
] |
1707.01495 | 19 | # e
# e
# for
# end for
HER may be seen as a form of implicit curriculum as the goals used for replay naturally shift from ones which are simple to achieve even by a random agent to more difficult ones. However, in contrast to explicit curriculum, HER does not require having any control over the distribution of initial environment states. Not only does HER learn with extremely sparse rewards, in our experiments it also performs better with sparse rewards than with shaped ones (See Sec. 4.4). These results are indicative of the practical challenges with reward shaping, and that shaped rewards would often constitute a compromise on the metric we truly care about (such as binary success/failure).
# 4 Experiments
The video presenting our experiments is available at https: //goo.gl/SMrQnI.
This section is organized as follows. In Sec. 4.1 we introduce multi-goal RL environments we use for the experiments as well as our training procedure. In Sec. 4.2 we compare the performance of DDPG with and without HER. In Sec. 4.3 we check if HER improves performance in the single-goal setup. In Sec. 4.4 we analyze the effects of using shaped reward functions. In Sec. 4.5 we compare different strategies for sampling additional goals for HER. In Sec. 4.6 we show the results of the experiments on the physical robot.
# 4.1 Environments | 1707.01495#19 | Hindsight Experience Replay | Dealing with sparse rewards is one of the biggest challenges in Reinforcement
Learning (RL). We present a novel technique called Hindsight Experience Replay
which allows sample-efficient learning from rewards which are sparse and binary
and therefore avoid the need for complicated reward engineering. It can be
combined with an arbitrary off-policy RL algorithm and may be seen as a form of
implicit curriculum.
We demonstrate our approach on the task of manipulating objects with a
robotic arm. In particular, we run experiments on three different tasks:
pushing, sliding, and pick-and-place, in each case using only binary rewards
indicating whether or not the task is completed. Our ablation studies show that
Hindsight Experience Replay is a crucial ingredient which makes training
possible in these challenging environments. We show that our policies trained
on a physics simulation can be deployed on a physical robot and successfully
complete the task. | http://arxiv.org/pdf/1707.01495 | Marcin Andrychowicz, Filip Wolski, Alex Ray, Jonas Schneider, Rachel Fong, Peter Welinder, Bob McGrew, Josh Tobin, Pieter Abbeel, Wojciech Zaremba | cs.LG, cs.AI, cs.NE, cs.RO | null | null | cs.LG | 20170705 | 20180223 | [
{
"id": "1511.05952"
},
{
"id": "1611.04717"
},
{
"id": "1703.06907"
},
{
"id": "1509.02971"
}
] |
1707.01495 | 20 | # 4.1 Environments
The are no standard environments for multi-goal RL and therefore we created our own environments. We decided to use manipulation environments based on an existing hardware robot to ensure that the challenges we face correspond as closely as possible to the real world. In all experiments we use a 7-DOF Fetch Robotics arm which has a two-fingered parallel gripper. The robot is simulated using the MuJoCo (Todorov et al., 2012) physics engine. The whole training procedure is performed in the simulation but we show in Sec. 4.6 that the trained policies perform well on the physical robot without any finetuning. | 1707.01495#20 | Hindsight Experience Replay | Dealing with sparse rewards is one of the biggest challenges in Reinforcement
Learning (RL). We present a novel technique called Hindsight Experience Replay
which allows sample-efficient learning from rewards which are sparse and binary
and therefore avoid the need for complicated reward engineering. It can be
combined with an arbitrary off-policy RL algorithm and may be seen as a form of
implicit curriculum.
We demonstrate our approach on the task of manipulating objects with a
robotic arm. In particular, we run experiments on three different tasks:
pushing, sliding, and pick-and-place, in each case using only binary rewards
indicating whether or not the task is completed. Our ablation studies show that
Hindsight Experience Replay is a crucial ingredient which makes training
possible in these challenging environments. We show that our policies trained
on a physics simulation can be deployed on a physical robot and successfully
complete the task. | http://arxiv.org/pdf/1707.01495 | Marcin Andrychowicz, Filip Wolski, Alex Ray, Jonas Schneider, Rachel Fong, Peter Welinder, Bob McGrew, Josh Tobin, Pieter Abbeel, Wojciech Zaremba | cs.LG, cs.AI, cs.NE, cs.RO | null | null | cs.LG | 20170705 | 20180223 | [
{
"id": "1511.05952"
},
{
"id": "1611.04717"
},
{
"id": "1703.06907"
},
{
"id": "1509.02971"
}
] |
1707.01495 | 21 | Figure 2: Different tasks: pushing (top row), sliding (middle row) and pick-and-place (bottom row). The red ball denotes the goal position.
Policies are represented as Multi-Layer Perceptrons (MLPs) with Rectified Linear Unit (ReLU) activation functions. Training is performed using the DDPG algorithm (Lillicrap et al., 2015) with Adam (Kingma and Ba, 2014) as the optimizer. For improved efficiency we use 8 workers which average the parameters after every update. See Appendix A for more details and the values of all hyperparameters.
We consider 3 different tasks:
1. Pushing. In this task a box is placed on a table in front of the robot and the task is to move it to the target location on the table. The robot fingers are locked to prevent grasping. The learned behaviour is a mixture of pushing and rolling.
2. Sliding. In this task a puck is placed on a long slippery table and the target position is outside of the robotâs reach so that it has to hit the puck with such a force that it slides and then stops in the appropriate place due to friction. | 1707.01495#21 | Hindsight Experience Replay | Dealing with sparse rewards is one of the biggest challenges in Reinforcement
Learning (RL). We present a novel technique called Hindsight Experience Replay
which allows sample-efficient learning from rewards which are sparse and binary
and therefore avoid the need for complicated reward engineering. It can be
combined with an arbitrary off-policy RL algorithm and may be seen as a form of
implicit curriculum.
We demonstrate our approach on the task of manipulating objects with a
robotic arm. In particular, we run experiments on three different tasks:
pushing, sliding, and pick-and-place, in each case using only binary rewards
indicating whether or not the task is completed. Our ablation studies show that
Hindsight Experience Replay is a crucial ingredient which makes training
possible in these challenging environments. We show that our policies trained
on a physics simulation can be deployed on a physical robot and successfully
complete the task. | http://arxiv.org/pdf/1707.01495 | Marcin Andrychowicz, Filip Wolski, Alex Ray, Jonas Schneider, Rachel Fong, Peter Welinder, Bob McGrew, Josh Tobin, Pieter Abbeel, Wojciech Zaremba | cs.LG, cs.AI, cs.NE, cs.RO | null | null | cs.LG | 20170705 | 20180223 | [
{
"id": "1511.05952"
},
{
"id": "1611.04717"
},
{
"id": "1703.06907"
},
{
"id": "1509.02971"
}
] |
1707.01495 | 22 | 3. Pick-and-place. This task is similar to pushing but the target position is in the air and the fingers are not locked. To make exploration in this task easier we recorded a single state in which the box is grasped and start half of the training episodes from this stateâ.
States: The state of the system is represented in the MuJoCo physics engine and consists of angles and velocities of all robot joints as well as positions, rotations and velocities (linear and angular) of all objects.
Goals: Goals describe the desired position of the object (a box or a puck depending on the task) with some fixed tolerance of ⬠ic. G = R® and f,(s) = [|g â Sobject| < â¬], where Sopject is the position of the object in the state s. The mapping from states to goals used in HER is simply m(s) = SobjectRewards: Unless stated otherwise we use binary and sparse rewards r(s, a, 9) = â[fg(sâ) = 0] where sâ if the state after the execution of the action a in the state s. We compare sparse and shaped reward functions in Sec. 4.4.
State-goal distributions: For all tasks the initial position of the gripper is fixed, while the initial position of the object and the target are randomized. See Appendix A for details. | 1707.01495#22 | Hindsight Experience Replay | Dealing with sparse rewards is one of the biggest challenges in Reinforcement
Learning (RL). We present a novel technique called Hindsight Experience Replay
which allows sample-efficient learning from rewards which are sparse and binary
and therefore avoid the need for complicated reward engineering. It can be
combined with an arbitrary off-policy RL algorithm and may be seen as a form of
implicit curriculum.
We demonstrate our approach on the task of manipulating objects with a
robotic arm. In particular, we run experiments on three different tasks:
pushing, sliding, and pick-and-place, in each case using only binary rewards
indicating whether or not the task is completed. Our ablation studies show that
Hindsight Experience Replay is a crucial ingredient which makes training
possible in these challenging environments. We show that our policies trained
on a physics simulation can be deployed on a physical robot and successfully
complete the task. | http://arxiv.org/pdf/1707.01495 | Marcin Andrychowicz, Filip Wolski, Alex Ray, Jonas Schneider, Rachel Fong, Peter Welinder, Bob McGrew, Josh Tobin, Pieter Abbeel, Wojciech Zaremba | cs.LG, cs.AI, cs.NE, cs.RO | null | null | cs.LG | 20170705 | 20180223 | [
{
"id": "1511.05952"
},
{
"id": "1611.04717"
},
{
"id": "1703.06907"
},
{
"id": "1509.02971"
}
] |
1707.01495 | 23 | State-goal distributions: For all tasks the initial position of the gripper is fixed, while the initial position of the object and the target are randomized. See Appendix A for details.
>This was necessary because we could not successfully train any policies for this task without using the demonstration state. We have later discovered that training is possible without this trick if only the goal position is sometimes on the table and sometimes in the air.
Observations: In this paragraph relative means relative to the current gripper position. The policy is given as input the absolute position of the gripper, the relative position of the object and the target*, as well as the distance between the fingers. The Q-function is additionally given the linear velocity of the gripper and fingers as well as relative linear and angular velocity of the object. We decided to restrict the input to the policy in order to make deployment on the physical robot easier.
Actions: of the problems we consider require gripper rotation and therefore we keep it fixed. Action space is 4-dimensional. Three dimensions specify the desired relative gripper position at the next timestep. We use MuJoCo constraints to move the gripper towards the desired position but Jacobian-based control could be used instead*. The last dimension specifies the desired distance between the 2 fingers which are position controlled. | 1707.01495#23 | Hindsight Experience Replay | Dealing with sparse rewards is one of the biggest challenges in Reinforcement
Learning (RL). We present a novel technique called Hindsight Experience Replay
which allows sample-efficient learning from rewards which are sparse and binary
and therefore avoid the need for complicated reward engineering. It can be
combined with an arbitrary off-policy RL algorithm and may be seen as a form of
implicit curriculum.
We demonstrate our approach on the task of manipulating objects with a
robotic arm. In particular, we run experiments on three different tasks:
pushing, sliding, and pick-and-place, in each case using only binary rewards
indicating whether or not the task is completed. Our ablation studies show that
Hindsight Experience Replay is a crucial ingredient which makes training
possible in these challenging environments. We show that our policies trained
on a physics simulation can be deployed on a physical robot and successfully
complete the task. | http://arxiv.org/pdf/1707.01495 | Marcin Andrychowicz, Filip Wolski, Alex Ray, Jonas Schneider, Rachel Fong, Peter Welinder, Bob McGrew, Josh Tobin, Pieter Abbeel, Wojciech Zaremba | cs.LG, cs.AI, cs.NE, cs.RO | null | null | cs.LG | 20170705 | 20180223 | [
{
"id": "1511.05952"
},
{
"id": "1611.04717"
},
{
"id": "1703.06907"
},
{
"id": "1509.02971"
}
] |
1707.01495 | 24 | Strategy S for sampling goals for replay: Unless stated otherwise HER uses replay with the goal corresponding to the final state in each episode, i.e. S(so,..., 87) = m(sr). We compare different strategies for choosing which goals to replay with in Sec. 4.5.
# 4.2 Does HER improve performance?
In order to verify if HER improves performance we evaluate DDPG with and without HER on all 3 tasks. Moreover, we compare against DDPG with count-based exploration® (Strehl and Littman, 2005; Kolter and Ng, 2009; Tang et al., 2016; Bellemare et al., 2016; Ostrovski et al., 2017). For HER we store each transition in the replay buffer twice: once with the goal used for the generation of the episode and once with the goal corresponding to the final state from the episode (we call this strategy final). In Sec. 4.5 we perform ablation studies of different strategies S for choosing goals for replay, here we include the best version from Sec. 4.5 in the plot for comparison. | 1707.01495#24 | Hindsight Experience Replay | Dealing with sparse rewards is one of the biggest challenges in Reinforcement
Learning (RL). We present a novel technique called Hindsight Experience Replay
which allows sample-efficient learning from rewards which are sparse and binary
and therefore avoid the need for complicated reward engineering. It can be
combined with an arbitrary off-policy RL algorithm and may be seen as a form of
implicit curriculum.
We demonstrate our approach on the task of manipulating objects with a
robotic arm. In particular, we run experiments on three different tasks:
pushing, sliding, and pick-and-place, in each case using only binary rewards
indicating whether or not the task is completed. Our ablation studies show that
Hindsight Experience Replay is a crucial ingredient which makes training
possible in these challenging environments. We show that our policies trained
on a physics simulation can be deployed on a physical robot and successfully
complete the task. | http://arxiv.org/pdf/1707.01495 | Marcin Andrychowicz, Filip Wolski, Alex Ray, Jonas Schneider, Rachel Fong, Peter Welinder, Bob McGrew, Josh Tobin, Pieter Abbeel, Wojciech Zaremba | cs.LG, cs.AI, cs.NE, cs.RO | null | null | cs.LG | 20170705 | 20180223 | [
{
"id": "1511.05952"
},
{
"id": "1611.04717"
},
{
"id": "1703.06907"
},
{
"id": "1509.02971"
}
] |
1707.01495 | 25 | == DDPG ââ DDPG+count-based exploration ââ- DDPG+HER ââ DDPG+HER (version from Sec. 4.5) pushing sliding pick-and-place 100% 100% 100% = 80% 80% 80% 60% | J 60% 60% 40% 40% 40% success rate 20% 20% 20% 0% 0% 0% 0 50 100 150 200 0 50 100 150 200 0 50 100 150 200 epoch number (every epoch = 800 episodes = 800x50 timesteps)
Figure 3: Learning curves for multi-goal setup. An episode is considered successful if the distance between the object and the goal at the end of the episode is less than 7cm for pushing and pick-and- place and less than 20cm for sliding. The results are averaged across 5 random seeds and shaded areas represent one standard deviation. The red curves correspond to the future strategy with k = 4 from Sec. 4.5 while the blue one corresponds to the final strategy.
From Fig. 3 it is clear that DDPG without HER is unable to solve any of the tasksâ and DDPG with count-based exploration is only able to make some progress on the sliding task. On the other hand, DDPG with HER solves all tasks almost perfectly. It confirms that HER is a crucial element which makes learning from sparse, binary rewards possible. | 1707.01495#25 | Hindsight Experience Replay | Dealing with sparse rewards is one of the biggest challenges in Reinforcement
Learning (RL). We present a novel technique called Hindsight Experience Replay
which allows sample-efficient learning from rewards which are sparse and binary
and therefore avoid the need for complicated reward engineering. It can be
combined with an arbitrary off-policy RL algorithm and may be seen as a form of
implicit curriculum.
We demonstrate our approach on the task of manipulating objects with a
robotic arm. In particular, we run experiments on three different tasks:
pushing, sliding, and pick-and-place, in each case using only binary rewards
indicating whether or not the task is completed. Our ablation studies show that
Hindsight Experience Replay is a crucial ingredient which makes training
possible in these challenging environments. We show that our policies trained
on a physics simulation can be deployed on a physical robot and successfully
complete the task. | http://arxiv.org/pdf/1707.01495 | Marcin Andrychowicz, Filip Wolski, Alex Ray, Jonas Schneider, Rachel Fong, Peter Welinder, Bob McGrew, Josh Tobin, Pieter Abbeel, Wojciech Zaremba | cs.LG, cs.AI, cs.NE, cs.RO | null | null | cs.LG | 20170705 | 20180223 | [
{
"id": "1511.05952"
},
{
"id": "1611.04717"
},
{
"id": "1703.06907"
},
{
"id": "1509.02971"
}
] |
1707.01495 | 26 | âThe target position is relative to the current object position.
>The successful deployment on a physical robot (Sec. 4.6) confirms that our control model produces movements which are reproducible on the physical robot despite not being fully physically plausible.
°
We discretize the state space and use an intrinsic reward of the form a/VN, where a is a hyper- parameter and N is the number of times the given state was visited. The discretization works as fol- lows. We take the relative position of the box and the target and then discretize every coordinate using a grid with a stepsize 6 which is a hyperparameter. We have performed a hyperparameter search over a ⬠{0.032, 0.064, 0.125, 0.25, 0.5, 1, 2, 4,8, 16,32}, B ⬠{1cm,2cm, 4cm, 8cm}. The best results were obtained using a = 1 and 6 = 1cm and these are the results we report.
7We also evaluated DQN (without HER) on our tasks and it was not able to solve any of them.
2 © % 3 8 8 s a | 1707.01495#26 | Hindsight Experience Replay | Dealing with sparse rewards is one of the biggest challenges in Reinforcement
Learning (RL). We present a novel technique called Hindsight Experience Replay
which allows sample-efficient learning from rewards which are sparse and binary
and therefore avoid the need for complicated reward engineering. It can be
combined with an arbitrary off-policy RL algorithm and may be seen as a form of
implicit curriculum.
We demonstrate our approach on the task of manipulating objects with a
robotic arm. In particular, we run experiments on three different tasks:
pushing, sliding, and pick-and-place, in each case using only binary rewards
indicating whether or not the task is completed. Our ablation studies show that
Hindsight Experience Replay is a crucial ingredient which makes training
possible in these challenging environments. We show that our policies trained
on a physics simulation can be deployed on a physical robot and successfully
complete the task. | http://arxiv.org/pdf/1707.01495 | Marcin Andrychowicz, Filip Wolski, Alex Ray, Jonas Schneider, Rachel Fong, Peter Welinder, Bob McGrew, Josh Tobin, Pieter Abbeel, Wojciech Zaremba | cs.LG, cs.AI, cs.NE, cs.RO | null | null | cs.LG | 20170705 | 20180223 | [
{
"id": "1511.05952"
},
{
"id": "1611.04717"
},
{
"id": "1703.06907"
},
{
"id": "1509.02971"
}
] |
1707.01495 | 27 | 7We also evaluated DQN (without HER) on our tasks and it was not able to solve any of them.
2 © % 3 8 8 s a
= - DDPG â DDPG+countbased exploration ââ DDPG+HER pushing sliding pick-and-place 100% 100% 100% 80% < 80% 80% 60% 60% 60% 40% 40% - 40% 20% 20% â 20% 0% 0% â 0% 0 50 100 150 200 0 50 100 150 200 0 50 100 150 200 epoch number (every epoch = 800 episodes = 800x50 timesteps)
Figure 4: Learning curves for the single-goal case.
# 4.3 Does HER improve performance even if there is only one goal we care about?
In this section we evaluate whether HER improves performance in the case where there is only one goal we care about. To this end, we repeat the experiments from the previous section but the goal state is identical in all episodes.
From Fig. 4 it is clear that DDPG+HER performs much better than pure DDPG even if the goal state is identical in all episodes. More importantly, comparing Fig. 3 and Fig. 4 we can also notice that HER learns faster if training episodes contain multiple goals, so in practice it is advisable to train on multiple goals even if we care only about one of them.
# 4.4 How does HER interact with reward shaping? | 1707.01495#27 | Hindsight Experience Replay | Dealing with sparse rewards is one of the biggest challenges in Reinforcement
Learning (RL). We present a novel technique called Hindsight Experience Replay
which allows sample-efficient learning from rewards which are sparse and binary
and therefore avoid the need for complicated reward engineering. It can be
combined with an arbitrary off-policy RL algorithm and may be seen as a form of
implicit curriculum.
We demonstrate our approach on the task of manipulating objects with a
robotic arm. In particular, we run experiments on three different tasks:
pushing, sliding, and pick-and-place, in each case using only binary rewards
indicating whether or not the task is completed. Our ablation studies show that
Hindsight Experience Replay is a crucial ingredient which makes training
possible in these challenging environments. We show that our policies trained
on a physics simulation can be deployed on a physical robot and successfully
complete the task. | http://arxiv.org/pdf/1707.01495 | Marcin Andrychowicz, Filip Wolski, Alex Ray, Jonas Schneider, Rachel Fong, Peter Welinder, Bob McGrew, Josh Tobin, Pieter Abbeel, Wojciech Zaremba | cs.LG, cs.AI, cs.NE, cs.RO | null | null | cs.LG | 20170705 | 20180223 | [
{
"id": "1511.05952"
},
{
"id": "1611.04717"
},
{
"id": "1703.06907"
},
{
"id": "1509.02971"
}
] |
1707.01495 | 28 | # 4.4 How does HER interact with reward shaping?
So far we only considered binary rewards of the form r(s,a,g) = â[|g â Sobject| > â¬]. In this section we check how the performance of DDPG with and without HER changes if we replace this reward with one which is shaped. We considered reward functions of the form r(s,a,g) = Alg â Sopject|â â |g â Sopject|â> where sâ is the state of the environment after the execution of the action a in the state s and A ⬠{0,1}, p ⬠{1, 2} are hyperparameters.
Fig. 5 shows the results. Surprisingly neither DDPG, nor DDPG+HER was able to successfully solve any of the tasks with any of these reward functions®.Our results are consistent with the fact that successful applications of RL to difficult manipulation tasks which does not use demonstrations usually have more complicated reward functions than the ones we tried (e.g. Popov et al. (2017)). | 1707.01495#28 | Hindsight Experience Replay | Dealing with sparse rewards is one of the biggest challenges in Reinforcement
Learning (RL). We present a novel technique called Hindsight Experience Replay
which allows sample-efficient learning from rewards which are sparse and binary
and therefore avoid the need for complicated reward engineering. It can be
combined with an arbitrary off-policy RL algorithm and may be seen as a form of
implicit curriculum.
We demonstrate our approach on the task of manipulating objects with a
robotic arm. In particular, we run experiments on three different tasks:
pushing, sliding, and pick-and-place, in each case using only binary rewards
indicating whether or not the task is completed. Our ablation studies show that
Hindsight Experience Replay is a crucial ingredient which makes training
possible in these challenging environments. We show that our policies trained
on a physics simulation can be deployed on a physical robot and successfully
complete the task. | http://arxiv.org/pdf/1707.01495 | Marcin Andrychowicz, Filip Wolski, Alex Ray, Jonas Schneider, Rachel Fong, Peter Welinder, Bob McGrew, Josh Tobin, Pieter Abbeel, Wojciech Zaremba | cs.LG, cs.AI, cs.NE, cs.RO | null | null | cs.LG | 20170705 | 20180223 | [
{
"id": "1511.05952"
},
{
"id": "1611.04717"
},
{
"id": "1703.06907"
},
{
"id": "1509.02971"
}
] |
1707.01495 | 29 | The following two reasons can cause shaped rewards to perform so poorly: (1) There is a huge discrepancy between what we optimize (i.e. a shaped reward function) and the success condition (i.e.: is the object within some radius from the goal at the end of the episode); (2) Shaped rewards penalize for inappropriate behaviour (e.g. moving the box in a wrong direction) which may hinder exploration. It can cause the agent to learn not to touch the box at all if it can not manipulate it precisely and we noticed such behaviour in some of our experiments.
Our results suggest that domain-agnostic reward shaping does not work well (at least in the simple forms we have tried). Of course for every problem there exists a reward which makes it easy (Ng et al., 1999) but designing such shaped rewards requires a lot of domain knowledge and may in some cases not be much easier than directly scripting the policy. This strengthens our belief that learning from sparse, binary rewards is an important problem.
# 4.5 How many goals should we replay each trajectory with and how to choose them?
In this section we experimentally evaluate different strategies (i.e. S in Alg. 1) for choosing goals to use with HER. So far the only additional goals we used for replay were the ones corresponding to
8 | 1707.01495#29 | Hindsight Experience Replay | Dealing with sparse rewards is one of the biggest challenges in Reinforcement
Learning (RL). We present a novel technique called Hindsight Experience Replay
which allows sample-efficient learning from rewards which are sparse and binary
and therefore avoid the need for complicated reward engineering. It can be
combined with an arbitrary off-policy RL algorithm and may be seen as a form of
implicit curriculum.
We demonstrate our approach on the task of manipulating objects with a
robotic arm. In particular, we run experiments on three different tasks:
pushing, sliding, and pick-and-place, in each case using only binary rewards
indicating whether or not the task is completed. Our ablation studies show that
Hindsight Experience Replay is a crucial ingredient which makes training
possible in these challenging environments. We show that our policies trained
on a physics simulation can be deployed on a physical robot and successfully
complete the task. | http://arxiv.org/pdf/1707.01495 | Marcin Andrychowicz, Filip Wolski, Alex Ray, Jonas Schneider, Rachel Fong, Peter Welinder, Bob McGrew, Josh Tobin, Pieter Abbeel, Wojciech Zaremba | cs.LG, cs.AI, cs.NE, cs.RO | null | null | cs.LG | 20170705 | 20180223 | [
{
"id": "1511.05952"
},
{
"id": "1611.04717"
},
{
"id": "1703.06907"
},
{
"id": "1509.02971"
}
] |
1707.01495 | 30 | 8
We also tried to rescale the distances, so that the range of rewards is similar as in the case of binary rewards, clipping big distances and adding a simple (linear or quadratic) term encouraging the gripper to move towards the object but none of these techniques have led to successful training.
-- DDPG â DDPG+HER} pushing sliding pick-and-place 100% 100% 100% 80% 80% 80% £ 60% 60% 60% 2 8 8 40% 40% 40% g a 20% 20% =e 20% | oles QO 0% 0% = 0 50 100 150 200 0 50 100 150 200 0 50 100 150 200 epoch number (every epoch = 800 episodes = 80x50 timesteps)
2
7 : ; _ , 24 Figure 5: Learning curves for the shaped reward r(s,a,g) = â|g â Sopject| (it performed best among the shaped rewards we have tried). Both algorithms fail on all tasks. | 1707.01495#30 | Hindsight Experience Replay | Dealing with sparse rewards is one of the biggest challenges in Reinforcement
Learning (RL). We present a novel technique called Hindsight Experience Replay
which allows sample-efficient learning from rewards which are sparse and binary
and therefore avoid the need for complicated reward engineering. It can be
combined with an arbitrary off-policy RL algorithm and may be seen as a form of
implicit curriculum.
We demonstrate our approach on the task of manipulating objects with a
robotic arm. In particular, we run experiments on three different tasks:
pushing, sliding, and pick-and-place, in each case using only binary rewards
indicating whether or not the task is completed. Our ablation studies show that
Hindsight Experience Replay is a crucial ingredient which makes training
possible in these challenging environments. We show that our policies trained
on a physics simulation can be deployed on a physical robot and successfully
complete the task. | http://arxiv.org/pdf/1707.01495 | Marcin Andrychowicz, Filip Wolski, Alex Ray, Jonas Schneider, Rachel Fong, Peter Welinder, Bob McGrew, Josh Tobin, Pieter Abbeel, Wojciech Zaremba | cs.LG, cs.AI, cs.NE, cs.RO | null | null | cs.LG | 20170705 | 20180223 | [
{
"id": "1511.05952"
},
{
"id": "1611.04717"
},
{
"id": "1703.06907"
},
{
"id": "1509.02971"
}
] |
1707.01495 | 31 | == noHER â= final â-®= random â@®= episode â®= future pushing sliding pick-and-place 1.0 I 1.0 DD ââ$â$â$»ââ 2 f @ 08 08 0.8 8 8 06 0.6 0.6 8 3 2 04 04 | 0.4 â % 3 2 20.2 02 02 . ee, âoâ 00 - - 0.0 â- 00 0.0 â----- ~~ 1 2 4 8 16 all 1 2 4 8 16 all 1 2 4 8 16 all pushing sliding pick-and-place 1.0 1.0 1.0 2 B08 08 0.8 ra 3 8 06 0.6 0.6 8 a o 04 â 04 04 S £ 202 0.2 0.2 & 0.0 Feta - 0.0 bo ee = 0.0 â----â -S = 1 2 4 8 16 all 1 2 4 8 16 all 1 2 4 8 16 all number of additional goals used to replay each transition with
Figure 6: Ablation study of different strategies for choosing additional goals for replay. The top row shows the highest (across the training epochs) test performance and the bottom row shows the average test performance across all training epochs. On the right top plot the curves for final, episode and future coincide as all these strategies achieve perfect performance on this task. | 1707.01495#31 | Hindsight Experience Replay | Dealing with sparse rewards is one of the biggest challenges in Reinforcement
Learning (RL). We present a novel technique called Hindsight Experience Replay
which allows sample-efficient learning from rewards which are sparse and binary
and therefore avoid the need for complicated reward engineering. It can be
combined with an arbitrary off-policy RL algorithm and may be seen as a form of
implicit curriculum.
We demonstrate our approach on the task of manipulating objects with a
robotic arm. In particular, we run experiments on three different tasks:
pushing, sliding, and pick-and-place, in each case using only binary rewards
indicating whether or not the task is completed. Our ablation studies show that
Hindsight Experience Replay is a crucial ingredient which makes training
possible in these challenging environments. We show that our policies trained
on a physics simulation can be deployed on a physical robot and successfully
complete the task. | http://arxiv.org/pdf/1707.01495 | Marcin Andrychowicz, Filip Wolski, Alex Ray, Jonas Schneider, Rachel Fong, Peter Welinder, Bob McGrew, Josh Tobin, Pieter Abbeel, Wojciech Zaremba | cs.LG, cs.AI, cs.NE, cs.RO | null | null | cs.LG | 20170705 | 20180223 | [
{
"id": "1511.05952"
},
{
"id": "1611.04717"
},
{
"id": "1703.06907"
},
{
"id": "1509.02971"
}
] |
1707.01495 | 32 | the final state of the environment and we will call this strategy final. Apart from it we consider the following strategies:
e future â replay with k random states which come from the same episode as the transition being replayed and were observed after it,
e episode â replay with k random states coming from the same episode as the transition being replayed,
e random â replay with k random states encountered so far in the whole training procedure.
All of these strategies have a hyperparameter k which controls the ratio of HER data to data coming from normal experience replay in the replay buffer.
The plots comparing different strategies and different values of k can be found in Fig. 6. We can see from the plots that all strategies apart from random solve pushing and pick-and-place almost perfectly regardless of the values of k. In all cases future with k equal 4 or 8 performs best and it is the only strategy which is able to solve the sliding task almost perfectly. The learning curves for | 1707.01495#32 | Hindsight Experience Replay | Dealing with sparse rewards is one of the biggest challenges in Reinforcement
Learning (RL). We present a novel technique called Hindsight Experience Replay
which allows sample-efficient learning from rewards which are sparse and binary
and therefore avoid the need for complicated reward engineering. It can be
combined with an arbitrary off-policy RL algorithm and may be seen as a form of
implicit curriculum.
We demonstrate our approach on the task of manipulating objects with a
robotic arm. In particular, we run experiments on three different tasks:
pushing, sliding, and pick-and-place, in each case using only binary rewards
indicating whether or not the task is completed. Our ablation studies show that
Hindsight Experience Replay is a crucial ingredient which makes training
possible in these challenging environments. We show that our policies trained
on a physics simulation can be deployed on a physical robot and successfully
complete the task. | http://arxiv.org/pdf/1707.01495 | Marcin Andrychowicz, Filip Wolski, Alex Ray, Jonas Schneider, Rachel Fong, Peter Welinder, Bob McGrew, Josh Tobin, Pieter Abbeel, Wojciech Zaremba | cs.LG, cs.AI, cs.NE, cs.RO | null | null | cs.LG | 20170705 | 20180223 | [
{
"id": "1511.05952"
},
{
"id": "1611.04717"
},
{
"id": "1703.06907"
},
{
"id": "1509.02971"
}
] |
1707.01495 | 33 | Figure 7: The pick-and-place policy deployed on the physical robot.
future with k = 4 can be found in Fig. 3. It confirms that the most valuable goals for replay are the ones which are going to be achieved in the near futureâ. Notice that increasing the values of k above 8 degrades performance because the fraction of normal replay data in the buffer becomes very low.
# 4.6 Deployment on a physical robot
We took a policy for the pick-and-place task trained in the simulator (version with the future strategy and k = 4 from Sec. 4.5) and deployed it on a physical fetch robot without any finetuning. The box position was predicted using a separately trained CNN using raw fetch head camera images. See Appendix B for details.
Initially the policy succeeded in 2 out of 5 trials. It was not robust to small errors in the box position estimation because it was trained on perfect state coming from the simulation. After retraining the policy with gaussian noise (std=Icm) added to observations!° the success rate increased to 5/5. The video showing some of the trials is available at https: //goo.g1/SMrQnI.
# 5 Related work | 1707.01495#33 | Hindsight Experience Replay | Dealing with sparse rewards is one of the biggest challenges in Reinforcement
Learning (RL). We present a novel technique called Hindsight Experience Replay
which allows sample-efficient learning from rewards which are sparse and binary
and therefore avoid the need for complicated reward engineering. It can be
combined with an arbitrary off-policy RL algorithm and may be seen as a form of
implicit curriculum.
We demonstrate our approach on the task of manipulating objects with a
robotic arm. In particular, we run experiments on three different tasks:
pushing, sliding, and pick-and-place, in each case using only binary rewards
indicating whether or not the task is completed. Our ablation studies show that
Hindsight Experience Replay is a crucial ingredient which makes training
possible in these challenging environments. We show that our policies trained
on a physics simulation can be deployed on a physical robot and successfully
complete the task. | http://arxiv.org/pdf/1707.01495 | Marcin Andrychowicz, Filip Wolski, Alex Ray, Jonas Schneider, Rachel Fong, Peter Welinder, Bob McGrew, Josh Tobin, Pieter Abbeel, Wojciech Zaremba | cs.LG, cs.AI, cs.NE, cs.RO | null | null | cs.LG | 20170705 | 20180223 | [
{
"id": "1511.05952"
},
{
"id": "1611.04717"
},
{
"id": "1703.06907"
},
{
"id": "1509.02971"
}
] |
1707.01495 | 34 | # 5 Related work
The technique of experience replay has been introduced in Lin (1992) and became very popular after it was used in the DQN agent playing Atari (Mnih et al., 2015). Prioritized experience replay (Schaul et al., 2015b) is an improvement to experience replay which prioritizes transitions in the replay buffer in order to speed up training. It it orthogonal to our work and both approaches can be easily combined.
Learning simultaneously policies for multiple tasks have been heavily explored in the context of policy search, e.g. Schmidhuber and Huber (1990); Caruana (1998); Da Silva et al. (2012); Kober et al. (2012); Devin et al. (2016); Pinto and Gupta (2016). Learning off-policy value functions for multiple tasks was investigated by Foster and Dayan (2002) and Sutton et al. (2011). Our work is most heavily based on Schaul et al. (2015a) who considers training a single neural network approximating multiple value functions. Learning simultaneously to perform multiple tasks has been also investigated for a long time in the context of Hierarchical Reinforcement Learning, e.g. Bakker and Schmidhuber (2004); Vezhnevets et al. (2017). | 1707.01495#34 | Hindsight Experience Replay | Dealing with sparse rewards is one of the biggest challenges in Reinforcement
Learning (RL). We present a novel technique called Hindsight Experience Replay
which allows sample-efficient learning from rewards which are sparse and binary
and therefore avoid the need for complicated reward engineering. It can be
combined with an arbitrary off-policy RL algorithm and may be seen as a form of
implicit curriculum.
We demonstrate our approach on the task of manipulating objects with a
robotic arm. In particular, we run experiments on three different tasks:
pushing, sliding, and pick-and-place, in each case using only binary rewards
indicating whether or not the task is completed. Our ablation studies show that
Hindsight Experience Replay is a crucial ingredient which makes training
possible in these challenging environments. We show that our policies trained
on a physics simulation can be deployed on a physical robot and successfully
complete the task. | http://arxiv.org/pdf/1707.01495 | Marcin Andrychowicz, Filip Wolski, Alex Ray, Jonas Schneider, Rachel Fong, Peter Welinder, Bob McGrew, Josh Tobin, Pieter Abbeel, Wojciech Zaremba | cs.LG, cs.AI, cs.NE, cs.RO | null | null | cs.LG | 20170705 | 20180223 | [
{
"id": "1511.05952"
},
{
"id": "1611.04717"
},
{
"id": "1703.06907"
},
{
"id": "1509.02971"
}
] |
1707.01495 | 35 | Our approach may be seen as a form of implicit curriculum learning (Elman, 1993; Bengio et al., 2009). While curriculum is now often used for training neural networks (e.g. Zaremba and Sutskever (2014); Graves et al. (2016)), the curriculum is almost always hand-crafted. The problem of automatic curriculum generation was approached by Schmidhuber (2004) who constructed an asymptotically optimal algorithm for this problem using program search. Another interesting approach is PowerPlay (Schmidhuber, 2013; Srivastava et al., 2013) which is a general framework for automatic task selection. Graves et al. (2017) consider a setup where there is a fixed discrete set of tasks and empirically evaluate different strategies for automatic curriculum generation in this settings. Another approach investigated by Sukhbaatar et al. (2017) and Held et al. (2017) uses self-play between the policy and a task-setter in order to automatically generate goal states which are on the border of what the current policy can achieve. Our approach is orthogonal to these techniques and can be combined with them.
°We have also tried replaying the goals which are close to the ones achieved in the near future but it has not performed better than the future strategy | 1707.01495#35 | Hindsight Experience Replay | Dealing with sparse rewards is one of the biggest challenges in Reinforcement
Learning (RL). We present a novel technique called Hindsight Experience Replay
which allows sample-efficient learning from rewards which are sparse and binary
and therefore avoid the need for complicated reward engineering. It can be
combined with an arbitrary off-policy RL algorithm and may be seen as a form of
implicit curriculum.
We demonstrate our approach on the task of manipulating objects with a
robotic arm. In particular, we run experiments on three different tasks:
pushing, sliding, and pick-and-place, in each case using only binary rewards
indicating whether or not the task is completed. Our ablation studies show that
Hindsight Experience Replay is a crucial ingredient which makes training
possible in these challenging environments. We show that our policies trained
on a physics simulation can be deployed on a physical robot and successfully
complete the task. | http://arxiv.org/pdf/1707.01495 | Marcin Andrychowicz, Filip Wolski, Alex Ray, Jonas Schneider, Rachel Fong, Peter Welinder, Bob McGrew, Josh Tobin, Pieter Abbeel, Wojciech Zaremba | cs.LG, cs.AI, cs.NE, cs.RO | null | null | cs.LG | 20170705 | 20180223 | [
{
"id": "1511.05952"
},
{
"id": "1611.04717"
},
{
"id": "1703.06907"
},
{
"id": "1509.02971"
}
] |
1707.01495 | 36 | °We have also tried replaying the goals which are close to the ones achieved in the near future but it has not performed better than the future strategy
âThe Q-function approximator was trained using exact observations. It does not have to be robust to noisy observations because it is not used during the deployment on the physical robot.
10
# 6 Conclusions
We introduced a novel technique called Hindsight Experience Replay which makes possible applying RL algorithms to problems with sparse and binary rewards. Our technique can be combined with an arbitrary off-policy RL algorithm and we experimentally demonstrated that with DQN and DDPG.
We showed that HER allows training policies which push, slide and pick-and-place objects with a robotic arm to the specified positions while the vanilla RL algorithm fails to solve these tasks. We also showed that the policy for the pick-and-place task performs well on the physical robot without any finetuning. As far as we know, it is the first time so complicated behaviours were learned using only sparse, binary rewards.
# Acknowledgments
We would like to thank Ankur Handa, Jonathan Ho, John Schulman, Matthias Plappert, Tim Salimans, and Vikash Kumar for providing feedback on the previous versions of this manuscript. We would also like to thank Rein Houthooft and the whole OpenAI team for fruitful discussions as well as Bowen Baker for performing some additional experiments.
# References | 1707.01495#36 | Hindsight Experience Replay | Dealing with sparse rewards is one of the biggest challenges in Reinforcement
Learning (RL). We present a novel technique called Hindsight Experience Replay
which allows sample-efficient learning from rewards which are sparse and binary
and therefore avoid the need for complicated reward engineering. It can be
combined with an arbitrary off-policy RL algorithm and may be seen as a form of
implicit curriculum.
We demonstrate our approach on the task of manipulating objects with a
robotic arm. In particular, we run experiments on three different tasks:
pushing, sliding, and pick-and-place, in each case using only binary rewards
indicating whether or not the task is completed. Our ablation studies show that
Hindsight Experience Replay is a crucial ingredient which makes training
possible in these challenging environments. We show that our policies trained
on a physics simulation can be deployed on a physical robot and successfully
complete the task. | http://arxiv.org/pdf/1707.01495 | Marcin Andrychowicz, Filip Wolski, Alex Ray, Jonas Schneider, Rachel Fong, Peter Welinder, Bob McGrew, Josh Tobin, Pieter Abbeel, Wojciech Zaremba | cs.LG, cs.AI, cs.NE, cs.RO | null | null | cs.LG | 20170705 | 20180223 | [
{
"id": "1511.05952"
},
{
"id": "1611.04717"
},
{
"id": "1703.06907"
},
{
"id": "1509.02971"
}
] |
1707.01495 | 37 | # References
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Bakker, B. and Schmidhuber, J. (2004). Hierarchical reinforcement learning based on subgoal discovery and subpolicy specialization. In Proc. of the 8-th Conf. on Intelligent Autonomous Systems, pages 438-445.
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Caruana, R. (1998). Multitask learning. In Learning to learn, pages 95-133. Springer. | 1707.01495#37 | Hindsight Experience Replay | Dealing with sparse rewards is one of the biggest challenges in Reinforcement
Learning (RL). We present a novel technique called Hindsight Experience Replay
which allows sample-efficient learning from rewards which are sparse and binary
and therefore avoid the need for complicated reward engineering. It can be
combined with an arbitrary off-policy RL algorithm and may be seen as a form of
implicit curriculum.
We demonstrate our approach on the task of manipulating objects with a
robotic arm. In particular, we run experiments on three different tasks:
pushing, sliding, and pick-and-place, in each case using only binary rewards
indicating whether or not the task is completed. Our ablation studies show that
Hindsight Experience Replay is a crucial ingredient which makes training
possible in these challenging environments. We show that our policies trained
on a physics simulation can be deployed on a physical robot and successfully
complete the task. | http://arxiv.org/pdf/1707.01495 | Marcin Andrychowicz, Filip Wolski, Alex Ray, Jonas Schneider, Rachel Fong, Peter Welinder, Bob McGrew, Josh Tobin, Pieter Abbeel, Wojciech Zaremba | cs.LG, cs.AI, cs.NE, cs.RO | null | null | cs.LG | 20170705 | 20180223 | [
{
"id": "1511.05952"
},
{
"id": "1611.04717"
},
{
"id": "1703.06907"
},
{
"id": "1509.02971"
}
] |
1707.01495 | 38 | Caruana, R. (1998). Multitask learning. In Learning to learn, pages 95-133. Springer.
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Learning (RL). We present a novel technique called Hindsight Experience Replay
which allows sample-efficient learning from rewards which are sparse and binary
and therefore avoid the need for complicated reward engineering. It can be
combined with an arbitrary off-policy RL algorithm and may be seen as a form of
implicit curriculum.
We demonstrate our approach on the task of manipulating objects with a
robotic arm. In particular, we run experiments on three different tasks:
pushing, sliding, and pick-and-place, in each case using only binary rewards
indicating whether or not the task is completed. Our ablation studies show that
Hindsight Experience Replay is a crucial ingredient which makes training
possible in these challenging environments. We show that our policies trained
on a physics simulation can be deployed on a physical robot and successfully
complete the task. | http://arxiv.org/pdf/1707.01495 | Marcin Andrychowicz, Filip Wolski, Alex Ray, Jonas Schneider, Rachel Fong, Peter Welinder, Bob McGrew, Josh Tobin, Pieter Abbeel, Wojciech Zaremba | cs.LG, cs.AI, cs.NE, cs.RO | null | null | cs.LG | 20170705 | 20180223 | [
{
"id": "1511.05952"
},
{
"id": "1611.04717"
},
{
"id": "1703.06907"
},
{
"id": "1509.02971"
}
] |
1707.01495 | 39 | Foster, D. and Dayan, P. (2002). Structure in the space of value functions. Machine Learning, 49(2):325-346.
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Learning (RL). We present a novel technique called Hindsight Experience Replay
which allows sample-efficient learning from rewards which are sparse and binary
and therefore avoid the need for complicated reward engineering. It can be
combined with an arbitrary off-policy RL algorithm and may be seen as a form of
implicit curriculum.
We demonstrate our approach on the task of manipulating objects with a
robotic arm. In particular, we run experiments on three different tasks:
pushing, sliding, and pick-and-place, in each case using only binary rewards
indicating whether or not the task is completed. Our ablation studies show that
Hindsight Experience Replay is a crucial ingredient which makes training
possible in these challenging environments. We show that our policies trained
on a physics simulation can be deployed on a physical robot and successfully
complete the task. | http://arxiv.org/pdf/1707.01495 | Marcin Andrychowicz, Filip Wolski, Alex Ray, Jonas Schneider, Rachel Fong, Peter Welinder, Bob McGrew, Josh Tobin, Pieter Abbeel, Wojciech Zaremba | cs.LG, cs.AI, cs.NE, cs.RO | null | null | cs.LG | 20170705 | 20180223 | [
{
"id": "1511.05952"
},
{
"id": "1611.04717"
},
{
"id": "1703.06907"
},
{
"id": "1509.02971"
}
] |
1707.01495 | 40 | Houthooft, R., Chen, X., Duan, Y., Schulman, J., De Turck, F., and Abbeel, P. (2016). Vime: Variational information maximizing exploration. In Advances in Neural Information Processing Systems, pages 1109- 1117.
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Learning (RL). We present a novel technique called Hindsight Experience Replay
which allows sample-efficient learning from rewards which are sparse and binary
and therefore avoid the need for complicated reward engineering. It can be
combined with an arbitrary off-policy RL algorithm and may be seen as a form of
implicit curriculum.
We demonstrate our approach on the task of manipulating objects with a
robotic arm. In particular, we run experiments on three different tasks:
pushing, sliding, and pick-and-place, in each case using only binary rewards
indicating whether or not the task is completed. Our ablation studies show that
Hindsight Experience Replay is a crucial ingredient which makes training
possible in these challenging environments. We show that our policies trained
on a physics simulation can be deployed on a physical robot and successfully
complete the task. | http://arxiv.org/pdf/1707.01495 | Marcin Andrychowicz, Filip Wolski, Alex Ray, Jonas Schneider, Rachel Fong, Peter Welinder, Bob McGrew, Josh Tobin, Pieter Abbeel, Wojciech Zaremba | cs.LG, cs.AI, cs.NE, cs.RO | null | null | cs.LG | 20170705 | 20180223 | [
{
"id": "1511.05952"
},
{
"id": "1611.04717"
},
{
"id": "1703.06907"
},
{
"id": "1509.02971"
}
] |
1707.01495 | 41 | Lillicrap, T. P., Hunt, J. J., Pritzel, A., Heess, N., Erez, T., Tassa, Y., Silver, D., and Wierstra, D. (2015). Continuous control with deep reinforcement learning. arXiv preprint arXiv:1509.02971.
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Learning (RL). We present a novel technique called Hindsight Experience Replay
which allows sample-efficient learning from rewards which are sparse and binary
and therefore avoid the need for complicated reward engineering. It can be
combined with an arbitrary off-policy RL algorithm and may be seen as a form of
implicit curriculum.
We demonstrate our approach on the task of manipulating objects with a
robotic arm. In particular, we run experiments on three different tasks:
pushing, sliding, and pick-and-place, in each case using only binary rewards
indicating whether or not the task is completed. Our ablation studies show that
Hindsight Experience Replay is a crucial ingredient which makes training
possible in these challenging environments. We show that our policies trained
on a physics simulation can be deployed on a physical robot and successfully
complete the task. | http://arxiv.org/pdf/1707.01495 | Marcin Andrychowicz, Filip Wolski, Alex Ray, Jonas Schneider, Rachel Fong, Peter Welinder, Bob McGrew, Josh Tobin, Pieter Abbeel, Wojciech Zaremba | cs.LG, cs.AI, cs.NE, cs.RO | null | null | cs.LG | 20170705 | 20180223 | [
{
"id": "1511.05952"
},
{
"id": "1611.04717"
},
{
"id": "1703.06907"
},
{
"id": "1509.02971"
}
] |
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Learning (RL). We present a novel technique called Hindsight Experience Replay
which allows sample-efficient learning from rewards which are sparse and binary
and therefore avoid the need for complicated reward engineering. It can be
combined with an arbitrary off-policy RL algorithm and may be seen as a form of
implicit curriculum.
We demonstrate our approach on the task of manipulating objects with a
robotic arm. In particular, we run experiments on three different tasks:
pushing, sliding, and pick-and-place, in each case using only binary rewards
indicating whether or not the task is completed. Our ablation studies show that
Hindsight Experience Replay is a crucial ingredient which makes training
possible in these challenging environments. We show that our policies trained
on a physics simulation can be deployed on a physical robot and successfully
complete the task. | http://arxiv.org/pdf/1707.01495 | Marcin Andrychowicz, Filip Wolski, Alex Ray, Jonas Schneider, Rachel Fong, Peter Welinder, Bob McGrew, Josh Tobin, Pieter Abbeel, Wojciech Zaremba | cs.LG, cs.AI, cs.NE, cs.RO | null | null | cs.LG | 20170705 | 20180223 | [
{
"id": "1511.05952"
},
{
"id": "1611.04717"
},
{
"id": "1703.06907"
},
{
"id": "1509.02971"
}
] |
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Learning (RL). We present a novel technique called Hindsight Experience Replay
which allows sample-efficient learning from rewards which are sparse and binary
and therefore avoid the need for complicated reward engineering. It can be
combined with an arbitrary off-policy RL algorithm and may be seen as a form of
implicit curriculum.
We demonstrate our approach on the task of manipulating objects with a
robotic arm. In particular, we run experiments on three different tasks:
pushing, sliding, and pick-and-place, in each case using only binary rewards
indicating whether or not the task is completed. Our ablation studies show that
Hindsight Experience Replay is a crucial ingredient which makes training
possible in these challenging environments. We show that our policies trained
on a physics simulation can be deployed on a physical robot and successfully
complete the task. | http://arxiv.org/pdf/1707.01495 | Marcin Andrychowicz, Filip Wolski, Alex Ray, Jonas Schneider, Rachel Fong, Peter Welinder, Bob McGrew, Josh Tobin, Pieter Abbeel, Wojciech Zaremba | cs.LG, cs.AI, cs.NE, cs.RO | null | null | cs.LG | 20170705 | 20180223 | [
{
"id": "1511.05952"
},
{
"id": "1611.04717"
},
{
"id": "1703.06907"
},
{
"id": "1509.02971"
}
] |
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Learning (RL). We present a novel technique called Hindsight Experience Replay
which allows sample-efficient learning from rewards which are sparse and binary
and therefore avoid the need for complicated reward engineering. It can be
combined with an arbitrary off-policy RL algorithm and may be seen as a form of
implicit curriculum.
We demonstrate our approach on the task of manipulating objects with a
robotic arm. In particular, we run experiments on three different tasks:
pushing, sliding, and pick-and-place, in each case using only binary rewards
indicating whether or not the task is completed. Our ablation studies show that
Hindsight Experience Replay is a crucial ingredient which makes training
possible in these challenging environments. We show that our policies trained
on a physics simulation can be deployed on a physical robot and successfully
complete the task. | http://arxiv.org/pdf/1707.01495 | Marcin Andrychowicz, Filip Wolski, Alex Ray, Jonas Schneider, Rachel Fong, Peter Welinder, Bob McGrew, Josh Tobin, Pieter Abbeel, Wojciech Zaremba | cs.LG, cs.AI, cs.NE, cs.RO | null | null | cs.LG | 20170705 | 20180223 | [
{
"id": "1511.05952"
},
{
"id": "1611.04717"
},
{
"id": "1703.06907"
},
{
"id": "1509.02971"
}
] |
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Learning (RL). We present a novel technique called Hindsight Experience Replay
which allows sample-efficient learning from rewards which are sparse and binary
and therefore avoid the need for complicated reward engineering. It can be
combined with an arbitrary off-policy RL algorithm and may be seen as a form of
implicit curriculum.
We demonstrate our approach on the task of manipulating objects with a
robotic arm. In particular, we run experiments on three different tasks:
pushing, sliding, and pick-and-place, in each case using only binary rewards
indicating whether or not the task is completed. Our ablation studies show that
Hindsight Experience Replay is a crucial ingredient which makes training
possible in these challenging environments. We show that our policies trained
on a physics simulation can be deployed on a physical robot and successfully
complete the task. | http://arxiv.org/pdf/1707.01495 | Marcin Andrychowicz, Filip Wolski, Alex Ray, Jonas Schneider, Rachel Fong, Peter Welinder, Bob McGrew, Josh Tobin, Pieter Abbeel, Wojciech Zaremba | cs.LG, cs.AI, cs.NE, cs.RO | null | null | cs.LG | 20170705 | 20180223 | [
{
"id": "1511.05952"
},
{
"id": "1611.04717"
},
{
"id": "1703.06907"
},
{
"id": "1509.02971"
}
] |
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13
# A Experiment details
In this section we provide more details on our experimental setup and hyperparameters used. | 1707.01495#46 | Hindsight Experience Replay | Dealing with sparse rewards is one of the biggest challenges in Reinforcement
Learning (RL). We present a novel technique called Hindsight Experience Replay
which allows sample-efficient learning from rewards which are sparse and binary
and therefore avoid the need for complicated reward engineering. It can be
combined with an arbitrary off-policy RL algorithm and may be seen as a form of
implicit curriculum.
We demonstrate our approach on the task of manipulating objects with a
robotic arm. In particular, we run experiments on three different tasks:
pushing, sliding, and pick-and-place, in each case using only binary rewards
indicating whether or not the task is completed. Our ablation studies show that
Hindsight Experience Replay is a crucial ingredient which makes training
possible in these challenging environments. We show that our policies trained
on a physics simulation can be deployed on a physical robot and successfully
complete the task. | http://arxiv.org/pdf/1707.01495 | Marcin Andrychowicz, Filip Wolski, Alex Ray, Jonas Schneider, Rachel Fong, Peter Welinder, Bob McGrew, Josh Tobin, Pieter Abbeel, Wojciech Zaremba | cs.LG, cs.AI, cs.NE, cs.RO | null | null | cs.LG | 20170705 | 20180223 | [
{
"id": "1511.05952"
},
{
"id": "1611.04717"
},
{
"id": "1703.06907"
},
{
"id": "1509.02971"
}
] |
1707.01495 | 47 | 13
# A Experiment details
In this section we provide more details on our experimental setup and hyperparameters used.
Bit-flipping experiment: We used a network with 1 hidden layer with 256 neurons. The length of each episode was equal to the number of bits and the episode was considered successful if the goal state was achieved at an arbitrary timestep during the episode. All other hyperparameters used were the same as in the case of DDPG experiments.
State-goal distributions: For all tasks the initial position of the gripper is fixed, for the pushing and sliding tasks it is located just above the table surface and for pushing it is located 20cm above the table. The object is placed randomly on the table in the 30cm x 30cm (20c x 20cm for sliding) square with the center directly under the gripper (both objects are 5cm wide). For pushing, the goal state is sampled uniformly from the same square as the box position. In the pick-and-place task the target is located in the air in order to force the robot to grasp (and not just push). The x and y coordinates of the goal position are sampled uniformly from the mentioned square and the height is sampled uniformly between 10cm and 45cm. For sliding the goal position is sampled from a 60cm x 60cm square centered 40cm away from the initial gripper position. For all tasks we discard initial state-goal pairs in which the goal is already satisfied. | 1707.01495#47 | Hindsight Experience Replay | Dealing with sparse rewards is one of the biggest challenges in Reinforcement
Learning (RL). We present a novel technique called Hindsight Experience Replay
which allows sample-efficient learning from rewards which are sparse and binary
and therefore avoid the need for complicated reward engineering. It can be
combined with an arbitrary off-policy RL algorithm and may be seen as a form of
implicit curriculum.
We demonstrate our approach on the task of manipulating objects with a
robotic arm. In particular, we run experiments on three different tasks:
pushing, sliding, and pick-and-place, in each case using only binary rewards
indicating whether or not the task is completed. Our ablation studies show that
Hindsight Experience Replay is a crucial ingredient which makes training
possible in these challenging environments. We show that our policies trained
on a physics simulation can be deployed on a physical robot and successfully
complete the task. | http://arxiv.org/pdf/1707.01495 | Marcin Andrychowicz, Filip Wolski, Alex Ray, Jonas Schneider, Rachel Fong, Peter Welinder, Bob McGrew, Josh Tobin, Pieter Abbeel, Wojciech Zaremba | cs.LG, cs.AI, cs.NE, cs.RO | null | null | cs.LG | 20170705 | 20180223 | [
{
"id": "1511.05952"
},
{
"id": "1611.04717"
},
{
"id": "1703.06907"
},
{
"id": "1509.02971"
}
] |
1707.01495 | 48 | Network architecture: Both actor and critic networks have 3 hidden layers with 64 hidden units in each layer. Hidden layers use ReLu activation function and the actor output layer uses tanh. The output of the tanh is then rescaled so that it lies in the range [â5cm, 5cm]. In order to prevent tanh saturation and vanishing gradients we add the square of the their preactivations to the actorâs cost function.
Training procedure: We train for 200 epochs. Each epoch consists of 50 cycles where each cycle consists of running the policy for 16 episodes and then performing 40 optimization steps on minibatches of size 128 sampled uniformly from a replay buffer consisting of 10° transitions. We update the target networks after every cycle using the decay coefficient of 0.95. Apart from using the target network for computing Q-targets for the critic we also use it in testing episodes as it is more stable than the main network. The whole training procedure is distributed over 8 threads. For the Adam optimization algorithm we use the learning rate of 0.001 and the default values from Tensorflow framework (Abadi et al., 2016) for the other hyperparameters. We use the discount factor of y = 0.98 for all transitions including the ones ending an episode. Moreover, we clip the targets used to train the critic to the range of possible values, i.e. [â cn 0). | 1707.01495#48 | Hindsight Experience Replay | Dealing with sparse rewards is one of the biggest challenges in Reinforcement
Learning (RL). We present a novel technique called Hindsight Experience Replay
which allows sample-efficient learning from rewards which are sparse and binary
and therefore avoid the need for complicated reward engineering. It can be
combined with an arbitrary off-policy RL algorithm and may be seen as a form of
implicit curriculum.
We demonstrate our approach on the task of manipulating objects with a
robotic arm. In particular, we run experiments on three different tasks:
pushing, sliding, and pick-and-place, in each case using only binary rewards
indicating whether or not the task is completed. Our ablation studies show that
Hindsight Experience Replay is a crucial ingredient which makes training
possible in these challenging environments. We show that our policies trained
on a physics simulation can be deployed on a physical robot and successfully
complete the task. | http://arxiv.org/pdf/1707.01495 | Marcin Andrychowicz, Filip Wolski, Alex Ray, Jonas Schneider, Rachel Fong, Peter Welinder, Bob McGrew, Josh Tobin, Pieter Abbeel, Wojciech Zaremba | cs.LG, cs.AI, cs.NE, cs.RO | null | null | cs.LG | 20170705 | 20180223 | [
{
"id": "1511.05952"
},
{
"id": "1611.04717"
},
{
"id": "1703.06907"
},
{
"id": "1509.02971"
}
] |
1707.01495 | 49 | Input scaling: Neural networks have problems dealing with inputs of different magnitudes and therefore it is crucial to scale them properly. To this end, we rescale inputs to neural networks so that they have mean zero and standard deviation equal to one and then clip them to the range [â5, 5]. Means and standard deviations used for rescaling are computed using all the observations encountered so far in the training.
Exploration: The behavioral policy we use for exploration works as follows. With probability 20% we sample (uniformly) a random action from the hypercube of valid actions. Otherwise, we take the output of the policy network and add independently to every coordinate normal noise with standard deviation equal to 5% of the total range of allowed values on this coordinate.
Simulation: Every episode consists of 50 environment timesteps, each of which consists of 10 MuJoCo steps with At = 0.002s. MuJoCo uses soft constraints for contacts and therefore object penetration is possible. It can be minimized by using a small timestep and more constraint solver epochs but it would slow down the simulation. We encountered some penetration in the pushing task (the agent learnt to push the box into the table in a way that it is pushed out by contact forces onto the target). In order to void this behaviour we added to the reward a term penalizing the squared depth of penetration for every contact pair.
14 | 1707.01495#49 | Hindsight Experience Replay | Dealing with sparse rewards is one of the biggest challenges in Reinforcement
Learning (RL). We present a novel technique called Hindsight Experience Replay
which allows sample-efficient learning from rewards which are sparse and binary
and therefore avoid the need for complicated reward engineering. It can be
combined with an arbitrary off-policy RL algorithm and may be seen as a form of
implicit curriculum.
We demonstrate our approach on the task of manipulating objects with a
robotic arm. In particular, we run experiments on three different tasks:
pushing, sliding, and pick-and-place, in each case using only binary rewards
indicating whether or not the task is completed. Our ablation studies show that
Hindsight Experience Replay is a crucial ingredient which makes training
possible in these challenging environments. We show that our policies trained
on a physics simulation can be deployed on a physical robot and successfully
complete the task. | http://arxiv.org/pdf/1707.01495 | Marcin Andrychowicz, Filip Wolski, Alex Ray, Jonas Schneider, Rachel Fong, Peter Welinder, Bob McGrew, Josh Tobin, Pieter Abbeel, Wojciech Zaremba | cs.LG, cs.AI, cs.NE, cs.RO | null | null | cs.LG | 20170705 | 20180223 | [
{
"id": "1511.05952"
},
{
"id": "1611.04717"
},
{
"id": "1703.06907"
},
{
"id": "1509.02971"
}
] |
1707.01495 | 50 | 14
Training time: Training for 200 epochs took us approximately 2.5h for pushing and the pick-and- place tasks and 6h for sliding (because physics simulation was slower for this task) using 8 cpu cores.
# B_ Deployment on the physical robot
We have trained a convolutional neural network (CNN) which predicts the box position given the raw image from the fetch head camera. The CNN was trained using only images coming from the Mujoco renderer. Despite the fact that training images were not photorealistic, the trained network performs well on real world data thanks to a high degree of randomization of textures, lightning and other visual parameters in training. This approach called domain randomization is described in more detail in Tobin et al. (2017).
At the beginning of each episode we initialize a simulated environment using the box position predicted by the CNN and robot state coming from the physical robot. From this point we run the policy in the simulator. After each timestep we send the simulated robot joint angles to the real one which is position-controlled and uses the simulated data as targets.
15 | 1707.01495#50 | Hindsight Experience Replay | Dealing with sparse rewards is one of the biggest challenges in Reinforcement
Learning (RL). We present a novel technique called Hindsight Experience Replay
which allows sample-efficient learning from rewards which are sparse and binary
and therefore avoid the need for complicated reward engineering. It can be
combined with an arbitrary off-policy RL algorithm and may be seen as a form of
implicit curriculum.
We demonstrate our approach on the task of manipulating objects with a
robotic arm. In particular, we run experiments on three different tasks:
pushing, sliding, and pick-and-place, in each case using only binary rewards
indicating whether or not the task is completed. Our ablation studies show that
Hindsight Experience Replay is a crucial ingredient which makes training
possible in these challenging environments. We show that our policies trained
on a physics simulation can be deployed on a physical robot and successfully
complete the task. | http://arxiv.org/pdf/1707.01495 | Marcin Andrychowicz, Filip Wolski, Alex Ray, Jonas Schneider, Rachel Fong, Peter Welinder, Bob McGrew, Josh Tobin, Pieter Abbeel, Wojciech Zaremba | cs.LG, cs.AI, cs.NE, cs.RO | null | null | cs.LG | 20170705 | 20180223 | [
{
"id": "1511.05952"
},
{
"id": "1611.04717"
},
{
"id": "1703.06907"
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"id": "1509.02971"
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1707.01067 | 1 | In this paper, we propose ELF, an Extensive, Lightweight and Flexible platform for fundamental reinforcement learning research. Using ELF, we implement a highly customizable real-time strategy (RTS) engine with three game environ- ments (Mini-RTS, Capture the Flag and Tower Defense). Mini-RTS, as a minia- ture version of StarCraft, captures key game dynamics and runs at 40K frame- per-second (FPS) per core on a laptop. When coupled with modern reinforcement learning methods, the system can train a full-game bot against built-in AIs end- to-end in one day with 6 CPUs and 1 GPU. In addition, our platform is ï¬exible in terms of environment-agent communication topologies, choices of RL methods, changes in game parameters, and can host existing C/C++-based game environ- ments like ALE [4]. Using ELF, we thoroughly explore training parameters and show that a network with Leaky ReLU [17] and Batch Normalization [11] cou- pled with long-horizon training and progressive curriculum beats the rule-based built-in AI more than 70% of the time in the full game of Mini-RTS. Strong per- formance is also achieved on | 1707.01067#1 | ELF: An Extensive, Lightweight and Flexible Research Platform for Real-time Strategy Games | In this paper, we propose ELF, an Extensive, Lightweight and Flexible
platform for fundamental reinforcement learning research. Using ELF, we
implement a highly customizable real-time strategy (RTS) engine with three game
environments (Mini-RTS, Capture the Flag and Tower Defense). Mini-RTS, as a
miniature version of StarCraft, captures key game dynamics and runs at 40K
frame-per-second (FPS) per core on a Macbook Pro notebook. When coupled with
modern reinforcement learning methods, the system can train a full-game bot
against built-in AIs end-to-end in one day with 6 CPUs and 1 GPU. In addition,
our platform is flexible in terms of environment-agent communication
topologies, choices of RL methods, changes in game parameters, and can host
existing C/C++-based game environments like Arcade Learning Environment. Using
ELF, we thoroughly explore training parameters and show that a network with
Leaky ReLU and Batch Normalization coupled with long-horizon training and
progressive curriculum beats the rule-based built-in AI more than $70\%$ of the
time in the full game of Mini-RTS. Strong performance is also achieved on the
other two games. In game replays, we show our agents learn interesting
strategies. ELF, along with its RL platform, is open-sourced at
https://github.com/facebookresearch/ELF. | http://arxiv.org/pdf/1707.01067 | Yuandong Tian, Qucheng Gong, Wenling Shang, Yuxin Wu, C. Lawrence Zitnick | cs.AI | NIPS 2017 oral | null | cs.AI | 20170704 | 20171110 | [
{
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},
{
"id": "1511.06410"
},
{
"id": "1609.05521"
},
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"id": "1602.01783"
}
] |
1707.01083 | 1 | # Megvii Inc (Face++) {zhangxiangyu,zxy,linmengxiao,sunjian}@megvii.com
# Abstract
We introduce an extremely computation-efï¬cient CNN architecture named Shufï¬eNet, which is designed specially for mobile devices with very limited computing power (e.g., 10-150 MFLOPs). The new architecture utilizes two new operations, pointwise group convolution and channel shuf- ï¬e, to greatly reduce computation cost while maintaining accuracy. Experiments on ImageNet classiï¬cation and MS COCO object detection demonstrate the superior perfor- mance of Shufï¬eNet over other structures, e.g. lower top-1 error (absolute 7.8%) than recent MobileNet [12] on Ima- geNet classiï¬cation task, under the computation budget of 40 MFLOPs. On an ARM-based mobile device, Shufï¬eNet achieves â¼13à actual speedup over AlexNet while main- taining comparable accuracy. | 1707.01083#1 | ShuffleNet: An Extremely Efficient Convolutional Neural Network for Mobile Devices | We introduce an extremely computation-efficient CNN architecture named
ShuffleNet, which is designed specially for mobile devices with very limited
computing power (e.g., 10-150 MFLOPs). The new architecture utilizes two new
operations, pointwise group convolution and channel shuffle, to greatly reduce
computation cost while maintaining accuracy. Experiments on ImageNet
classification and MS COCO object detection demonstrate the superior
performance of ShuffleNet over other structures, e.g. lower top-1 error
(absolute 7.8%) than recent MobileNet on ImageNet classification task, under
the computation budget of 40 MFLOPs. On an ARM-based mobile device, ShuffleNet
achieves ~13x actual speedup over AlexNet while maintaining comparable
accuracy. | http://arxiv.org/pdf/1707.01083 | Xiangyu Zhang, Xinyu Zhou, Mengxiao Lin, Jian Sun | cs.CV | null | null | cs.CV | 20170704 | 20171207 | [
{
"id": "1602.07360"
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"id": "1611.06473"
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"id": "1502.03167"
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"id": "1503.02531"
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"id": "1602.07261"
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"id": "1608.04337"
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"id": "1606.06160"
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"id": "1702.03044"
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"id": "1608.08021"
},
{
"id": "1710.05941"
},
{
"id": "1707.07012"
},
{
"id": "1611.05431"
},
{
"id": "1603.04467"
},
{
"id": "1704.04861"
},
{
"id": "1610.02357"
},
{
"id": "1709.01507"
},
{
"id": "1510.00149"
}
] |
1707.01083 | 2 | tions to reduce computation complexity of 1 à 1 convolu- tions. To overcome the side effects brought by group con- volutions, we come up with a novel channel shufï¬e opera- tion to help the information ï¬owing across feature channels. Based on the two techniques, we build a highly efï¬cient ar- chitecture called Shufï¬eNet. Compared with popular struc- tures like [30, 9, 40], for a given computation complexity budget, our Shufï¬eNet allows more feature map channels, which helps to encode more information and is especially critical to the performance of very small networks.
We evaluate our models on the challenging ImageNet classiï¬cation [4, 29] and MS COCO object detection [23] tasks. A series of controlled experiments shows the effec- tiveness of our design principles and the better performance over other structures. Compared with the state-of-the-art architecture MobileNet [12], Shufï¬eNet achieves superior performance by a signiï¬cant margin, e.g. absolute 7.8% lower ImageNet top-1 error at level of 40 MFLOPs.
# 1. Introduction | 1707.01083#2 | ShuffleNet: An Extremely Efficient Convolutional Neural Network for Mobile Devices | We introduce an extremely computation-efficient CNN architecture named
ShuffleNet, which is designed specially for mobile devices with very limited
computing power (e.g., 10-150 MFLOPs). The new architecture utilizes two new
operations, pointwise group convolution and channel shuffle, to greatly reduce
computation cost while maintaining accuracy. Experiments on ImageNet
classification and MS COCO object detection demonstrate the superior
performance of ShuffleNet over other structures, e.g. lower top-1 error
(absolute 7.8%) than recent MobileNet on ImageNet classification task, under
the computation budget of 40 MFLOPs. On an ARM-based mobile device, ShuffleNet
achieves ~13x actual speedup over AlexNet while maintaining comparable
accuracy. | http://arxiv.org/pdf/1707.01083 | Xiangyu Zhang, Xinyu Zhou, Mengxiao Lin, Jian Sun | cs.CV | null | null | cs.CV | 20170704 | 20171207 | [
{
"id": "1602.07360"
},
{
"id": "1611.06473"
},
{
"id": "1502.03167"
},
{
"id": "1503.02531"
},
{
"id": "1602.07261"
},
{
"id": "1608.04337"
},
{
"id": "1606.06160"
},
{
"id": "1702.03044"
},
{
"id": "1608.08021"
},
{
"id": "1710.05941"
},
{
"id": "1707.07012"
},
{
"id": "1611.05431"
},
{
"id": "1603.04467"
},
{
"id": "1704.04861"
},
{
"id": "1610.02357"
},
{
"id": "1709.01507"
},
{
"id": "1510.00149"
}
] |
1707.01067 | 3 | # Introduction
Game environments are commonly used for research in Reinforcement Learning (RL), i.e. how to train intelligent agents to behave properly from sparse rewards [4, 6, 5, 14, 29]. Compared to the real world, game environments offer an inï¬nite amount of highly controllable, fully reproducible, and automatically labeled data. Ideally, a game environment for fundamental RL research is:
⢠Extensive: The environment should capture many diverse aspects of the real world, such as rich dynamics, partial information, delayed/long-term rewards, concurrent actions with different granularity, etc. Having an extensive set of features and properties increases the potential for trained agents to generalize to diverse real-world scenarios.
⢠Lightweight: A platform should be fast and capable of generating samples hundreds or thousands of times faster than real-time with minimal computational resources (e.g., a sin- gle machine). Lightweight and efï¬cient platforms help accelerate academic research of RL algorithms, particularly for methods which are heavily data-dependent.
⢠Flexible: A platform that is easily customizable at different levels, including rich choices of environment content, easy manipulation of game parameters, accessibility of internal variables, and ï¬exibility of training architectures. All are important for fast exploration of different algorithms. For example, changing environment parameters [35], as well as using internal data [15, 19] have been shown to substantially accelerate training. | 1707.01067#3 | ELF: An Extensive, Lightweight and Flexible Research Platform for Real-time Strategy Games | In this paper, we propose ELF, an Extensive, Lightweight and Flexible
platform for fundamental reinforcement learning research. Using ELF, we
implement a highly customizable real-time strategy (RTS) engine with three game
environments (Mini-RTS, Capture the Flag and Tower Defense). Mini-RTS, as a
miniature version of StarCraft, captures key game dynamics and runs at 40K
frame-per-second (FPS) per core on a Macbook Pro notebook. When coupled with
modern reinforcement learning methods, the system can train a full-game bot
against built-in AIs end-to-end in one day with 6 CPUs and 1 GPU. In addition,
our platform is flexible in terms of environment-agent communication
topologies, choices of RL methods, changes in game parameters, and can host
existing C/C++-based game environments like Arcade Learning Environment. Using
ELF, we thoroughly explore training parameters and show that a network with
Leaky ReLU and Batch Normalization coupled with long-horizon training and
progressive curriculum beats the rule-based built-in AI more than $70\%$ of the
time in the full game of Mini-RTS. Strong performance is also achieved on the
other two games. In game replays, we show our agents learn interesting
strategies. ELF, along with its RL platform, is open-sourced at
https://github.com/facebookresearch/ELF. | http://arxiv.org/pdf/1707.01067 | Yuandong Tian, Qucheng Gong, Wenling Shang, Yuxin Wu, C. Lawrence Zitnick | cs.AI | NIPS 2017 oral | null | cs.AI | 20170704 | 20171110 | [
{
"id": "1605.02097"
},
{
"id": "1511.06410"
},
{
"id": "1609.05521"
},
{
"id": "1602.01783"
}
] |
1707.01083 | 3 | # 1. Introduction
Building deeper and larger convolutional neural net- works (CNNs) is a primary trend for solving major visual recognition tasks [21, 9, 33, 5, 28, 24]. The most accu- rate CNNs usually have hundreds of layers and thousands of channels [9, 34, 32, 40], thus requiring computation at billions of FLOPs. This report examines the opposite ex- treme: pursuing the best accuracy in very limited compu- tational budgets at tens or hundreds of MFLOPs, focusing on common mobile platforms such as drones, robots, and smartphones. Note that many existing works [16, 22, 43, 42, 38, 27] focus on pruning, compressing, or low-bit represent- ing a âbasicâ network architecture. Here we aim to explore a highly efï¬cient basic architecture specially designed for our desired computing ranges. | 1707.01083#3 | ShuffleNet: An Extremely Efficient Convolutional Neural Network for Mobile Devices | We introduce an extremely computation-efficient CNN architecture named
ShuffleNet, which is designed specially for mobile devices with very limited
computing power (e.g., 10-150 MFLOPs). The new architecture utilizes two new
operations, pointwise group convolution and channel shuffle, to greatly reduce
computation cost while maintaining accuracy. Experiments on ImageNet
classification and MS COCO object detection demonstrate the superior
performance of ShuffleNet over other structures, e.g. lower top-1 error
(absolute 7.8%) than recent MobileNet on ImageNet classification task, under
the computation budget of 40 MFLOPs. On an ARM-based mobile device, ShuffleNet
achieves ~13x actual speedup over AlexNet while maintaining comparable
accuracy. | http://arxiv.org/pdf/1707.01083 | Xiangyu Zhang, Xinyu Zhou, Mengxiao Lin, Jian Sun | cs.CV | null | null | cs.CV | 20170704 | 20171207 | [
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"id": "1608.08021"
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"id": "1707.07012"
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"id": "1603.04467"
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"id": "1610.02357"
},
{
"id": "1709.01507"
},
{
"id": "1510.00149"
}
] |
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