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Question: Exploration in sparse reward reinforcement learning remains an open challenge. Many state-of-the-art methods use intrinsic motivation to complement the sparse extrinsic reward signal, giving the agent more opportunities to receive feedback during exploration. Commonly these signals are added as bonus rewards, which in a mixture policy that neither conducts exploration nor task fulfillment resolutely. In this paper, we instead learn separate intrinsic and extrinsic task policies and schedule between these different drives to accelerate exploration and stabilize learning. Moreover, we introduce a new type of intrinsic reward denoted as successor feature control (SFC), which is general and not task-specific. It takes into account statistics over complete trajectories and thus differs from previous methods that only use local information to evaluate intrinsic motivation. We evaluate our proposed scheduled intrinsic drive (SID) agent using three different environments with pure visual inputs: VizDoom, DeepMind Lab and DeepMind Control Suite. The show a substantially improved exploration efficiency with SFC and the hierarchical usage of the intrinsic drives. A video of our experimental can be found at https://gofile.io/?c=HpEwTd. Reinforcement learning (RL) agents learn on evaluative feedback (reward signals) instead of instructive feedback (ground truth labels), which takes the process of automating the development of intelligent problem-solving agents one step further . With deep networks as powerful function approximators bringing traditional RL into high-dimensional domains, deep reinforcement learning (DRL) has shown great potential (; ;). However, the success of DRL often relies on carefully shaped dense extrinsic reward signals. Although shaping extrinsic rewards can greatly support the agent in finding solutions and shortening the interaction time, designing such dense extrinsic signals often requires substantial domain knowledge, and calculating them typically requires ground truth state information, both of which is hard to obtain in the context of robots acting in the real world. When not carefully designed, the reward shape could sometimes serve as bias or even distractions and could potentially hinder the discovery of optimal solutions. More importantly, learning on dense extrinsic rewards goes backwards on the progress of reducing supervision and could prevent the agent from taking full advantage of the RL framework. In this paper, we consider terminal reward RL settings, where a signal is only given when the final goal is achieved. When learning with only an extrinsic terminal reward indicating the task at hand, intelligent agents are given the opportunity to potentially discover optimal solutions even out of the scope of the well established domain knowledge. However, in many real-world problems defining a task only by a terminal reward means that the learning signal can be extremely sparse. The RL agent would have no clue about what task to accomplish until it receives the terminal reward for the first time by chance. Therefore in those scenarios guided and structured exploration is crucial, which is where intrinsically-motivated exploration has recently gained great success (; b). Most commonly in current state-of-the-art approaches, an intrinsic reward is added as a reward bonus to the extrinsic reward. Maximizing this combined reward signal, however, in a mixture policy that neither acts greedily with regard to extrinsic reward max-imization nor to exploration. Furthermore, the non-stationary nature of the intrinsic signals could potentially lead to unstable learning on the combined reward. In addition, current state-of-the-art methods have been mostly looking at local information calculated out of 1-step lookahead for the estimation of the intrinsic rewards, e.g. one step prediction error , or network distillation error of the next state (b). Although those intrinsic signals can be propagated back to earlier states with temporal difference (TD) learning, it is not clear that this in optimal long-term exploration. We seek to address the aforementioned issues as follows: 1. We propose a hierarchical agent scheduled intrinsic drive (SID) that focuses on one motivation at a time: It learns two separate policies which maximize the extrinsic and intrinsic rewards respectively. A high-level scheduler periodically selects to follow either the extrinsic or the intrinsic policy to gather experiences. Disentangling the two policies allows the agent to faithfully conduct either pure exploration or pure extrinsic task fulfillment. Moreover, scheduling (even within an episode) implicitly increases the behavior policy space exponentially, which drastically differs from previous methods where the behavior policy could only change slowly due to the incremental nature of TD learning. 2. We introduce successor feature control (SFC), a novel intrinsic reward that is based on the concept of successor features. This feature representation characterizes states through the features of all its successor states instead of looking at local information only. This implicitly makes our method temporarily extended, which enables more structured and farsighted exploration that is crucial in exploration-challenging environments. We note that both the proposed intrinsic reward SFC and the hierarchical exploration framework SID are without any task-specific components, and can be incorporated into existing DRL methods with minimal computation overhead. We present experimental in three sets of environments, evaluating our proposed agent in the domains of visual navigation and control from pixels, as well as its capabilities of finding optimal solutions under distraction. Intrinsic Motivation and Auxiliary Tasks Intrinsic motivation can be defined as agents conducting actions purely out of the satisfaction of its internal rewarding system rather than the extrinsic rewards . There exist various forms of intrinsic motivation and they have achieved substantial improvement in guiding exploration for DRL, in tasks where extrinsic signals are sparse or missing altogether. proposed to evaluate curiosity, one of the most widely used kinds of intrinsic motivation, with the 1-step prediction error of the features of the next state made by a forward dynamics model. Their ICM module has been shown to work well in visual domains including first-person view navigation. Since ICM is potentially susceptible to stochastic transitions (a), Burda et al. (2018b) propose as a reward bonus the error of predicting the features of the current state output by a randomly initialized fixed embedding network. The value function is decomposed for extrinsic and intrinsic reward, but different to us a single mixture policy is learned. Another form of curiosity, learning progress or the change in the prediction error, has been connected to count-based exploration via a pseudo-count and has also been used as a reward bonus. propose to train a reachability network, which gives out a reward based on whether the current state is reachable within a certain amount of steps from any state in the current episode. Similar to our proposed SFC, their intrinsic motivation is related to choosing states that could lead to novel trajectories. However, we use two different distance metrics, theirs is explicitly learned to be proportional to the time step differences while ours is based on successor features which measures two states by the difference of the average feature activations of future trajectories. Moreover, their method rewards states with high distance to the states in the current episode while our method rewards states with high distance to the states also from past trajectories, as the successor features are trained from samples of the replay buffer. Auxiliary tasks have been proposed for learning more representative and distinguishable features. add depth prediction and loop closure prediction as auxiliary tasks for learning the features. learn separate policies for maximizing pixel changes (pixel control) and activating units of a specific hidden layer (feature control). However, their proposed UNREAL agent never follows those auxiliary policies as they are only used to learn more suitable features for the main extrinsic task. Hierarchical RL Various HRL approaches have been proposed (a; ; ;). In the context of intrinsic motivation, feature control has been adopted into a hierarchical setting , in which options are constructed for altering given features. However, they report that a flat policy trained on the intrinsic bonus achieves similar performance to the hierarchical agent. Our hierarchical design is perhaps inspired mostly by the work of. Unlike other HRL approaches that try to learn a set of options to construct the optimal policy, their proposed SAC agent aims to learn one flat policy that maximizes the extrinsic reward. While SAC schedules between following the extrinsic task and a set of pre-defined auxiliary tasks such as maximizing touch sensor readings or translation velocity, in this paper we investigate scheduling between the extrinsic task and intrinsic motivation that is general and not task-specific. A concurrent work along this line is presented by. Successor Representation The successor representation (SR) was first introduced to improve generalization in TD learning . While previous works extended SR to the deep setting for better generalized navigation and control algorithms across similar environments and changing goals (b; ;), we focus on its temporarily extended property to accelerate exploration. SR has also been investigated under the options framework. When using SR to measure the intrinsic motivation, the most relevant work to ours is that of. They also design a task-independent intrinsic reward based on SR, however they rely on the concept of count-based exploration and propose a reward bonus, that vastly differs from ours. Their bonus is inverse proportional to the norm of the SR while our formulation rewards change in the SR of two successive states. We will present our proposed method in the next section. We use the RL framework for learning and decision-making under uncertainty. It is formalized by Markov decision processes (MDPs) defined by the tuple S, A, p, r, γ. At time step t the agent samples an action a ∈ A according to policy π(·|s), which depends on its current state s ∈ S. The agent receives a scalar reward r ∈ R and transits to the next state s ∈ S. The distribution of the corresponding state, action and reward process (S t, A t, R t+1) is determined by the distribution of the initial state S 0, the transition operator p and the policy π. The goal of the agent is to find a policy that maximizes the expectation of the sum of discounted rewards T k=0 γ k R t+k+1. We seek to speed up learning in sparse reward RL, where the reward signal is uninformative for almost all transitions. We set the focus on terminal reward scenarios, where the agent only receives a single reward of +1 for successfully accomplishing the task and 0 otherwise. We will first introduce our proposed intrinsic reward successor feature control (SFC) (3.1,3.2), then present our proposed hierachical framework for accelerating intrinsically motivated exploration, which we denote as scheduled intrinsic drive (SID) (Sec.3.3, 3.4). In order to encode long-term statistics into the design of intrinsic rewards for far-sighted exploration, we build on the formulation of successor represention (SR), which introduces a temporally extended view of the states. introduced the idea of representing a state s by the occupancies of all other states from a process starting in s following a fixed policy π, where the occupancies denote the average number of time steps the state process stays in each state per episode. ). The agent starts at the red cross and transitions to an adjacent state at each time step. The goal is to explore the four rooms when no extrinsic reward is provided. In a) each state is annotated by its SD (Eq.3) to the starting state and b) shows for each state the highest possible SFC reward (Eq.4) for a one-step transition from it. Here the successor features are learned using a random walk. c) and d) show a comparison between visitation counts of each state from a random agent and an agent that uses the SFC rewards for control via Q-learning. In the latter case the successor features are learned from scratch via TD. In this environment, the agent receives high rewards for crossing bottleneck states, when the SF are learned beforehand, using a random policy. But even when the SF are learned during exploration, bottleneck states are still visited disproportionately high. Furthermore the intrinsic reward greatly improves exploration compared to a random agent. For implementation details see Appendix. D.4 features (SF) (b;) extend the concept to an arbitrary feature embedding φ: S → R m. For a fixed policy π and embedding φ the SF is defined by the |m|-dimensional vector Analogously, the SF represent the average discounted feature activations, when starting in s and following π. They can be learned by temporal difference (TD) updates SF have several interesting properties which make them appealing as a basis for an intrinsic reward signal: 1) They can be learned even in the absence of extrinsic rewards and without learning a transition model and therefore combine advantages of model-based and model-free RL . 2) They can be learned via computationally efficient TD. 3) They capture the expected feature activations for complete episodes. Therefore they contain information even of spatially and temporarily distant states which might help for effective far-sighted exploration. Given the discussion, we introduce the successor distance (SD) metric that measures the distance between states by the similarity of their SF Fig.1 a) shows an example of the successor distance metric in the tabular case. There the SD roughly correlates to the length of the shortest path between the states. Using this metric to evaluate the intrinsic motivation, one choice could be to use the SD to a fixed anchor state as the intrinsic reward, which depends heavily on the anchor position. Even when a sensible choice for the anchor can be found, e.g. the initial state of an episode, the SDs of distant states from the anchor assimilate. For a pair of states with a fixed spatial distance, their SD is higher when they are located in different rooms and the SD increases substantially when crossing rooms. Therefore the metric might capture the connectivity of the underlying state space. This observation motivates us to define the intrinsic reward successor feature control (SFC) as the squared SD of a pair of consecutive states A high SFC reward indicates a big change in the future feature activations when π is followed. We argue this big change is a strong indicator of bottleneck states, since in bottlenecks a minor change in the action selection can lead to a vastly different trajectory being taken. Fig.1b ) shows that those highly rewarding states under SFC and the true bottlenecks agree, which can be very valuable for exploration . The classical way of adding the intrinsic reward to the extrinsic reward has several drawbacks. First, the final policy is not trained to maximize the actual objective but a mixed version. Second, the intrinsic reward signal is usually changing over time. Including this non-stationary signal in the overall reward can make learning of the actual task unstable. Furthermore, the performance is often extremely sensitive to the scaling of the intrinsic reward relative to the extrinsic and hence it has to be tuned very carefully for every environment. To overcome these issues we propose scheduled intrinsic drive (SID), which learns two separate policies, one for each reward signal. During each episode the scheduler samples several times which of the two policies to follow for the next time steps. Each policy is trained off-policy from all of the transitions irrespective of which policy collected the data. As SID does not add the two reward signals no scaling parameter is needed. A policy is learned that exclusively maximizes extrinsic reward and hence neither the final policy nor the learning process is disturbed by the intrinsic reward. At the same time exploration is ensured as there is experience collected by the policy that learns from the intrinsic reward. Furthermore, scheduling can help exploration as each policy is acted on for an extended time interval, allowing long-term exploration instead of local exploration. Besides that the agent is less susceptible to always go to a nearby small reward instead of looking for other larger rewards that maybe further away. A mixture policy might be attracted to the small reward while with SID the exploration policy is followed for several timesteps which can bring the agent to new states with larger rewards that it did not know of before. We investigated several types of high-level schedulers, however, none of them consistently outperforms a random one. We present possible explanations why a random scheduler already performs well and present them in Appendix F along with the different scheduler choices we tested. Our proposed method can be combined with an any approach that allows off-policy learning. This section describes an instantiation of the SID framework when using Ape-X DQN as a basic offpolicy DRL algorithm with SFC as the intrinsic reward, which we used for all experiments. We depict this algorithm instance in Appendix Figure 8 and more details are provided in Appendix C. The algorithm is composed of: • A Q-Net {θ ϕ, θ E, θ I}: Contains a shared embedding θ ϕ and two Q-value output heads θ E (extrinsic) and θ I (intrinsic). • A SF-Net {θ φ, θ ψ}: Contains an embedding θ φ and a successor feature head θ ψ. θ φ is initialized randomly and kept fixed during training. The output of SF-Net is used to calculate the SFC intrinsic reward (Eq.4). The SF-net is trained with the samples of the replay buffer, which contains the experience generated by the behavior policy. • A high-level scheduler: Instantiated in each actor, selects which policy to follow (extrinsic or intrinsic) after a fixed number of environment steps (max episode length/M). The scheduler randomly picks one of the tasks with equal probability. • N parallel actors (N = 8): Each actor instantiates its own copy of the environment, periodically copies the latest model from the learner. We learn from K-step targets (K = 5), so each actor at each environment step stores (s t−K, a t−K, K k=1 γ k−1 r t−K+k, s t) into a shared replay buffer. Each actor will act according to either the extrinsic or the intrinsic policy based on the current task selected by its scheduler. • A learner: Learns the Q-Net (θ E and θ I are learned with the extrinsic and intrinsic reward respectively) and the SF-Net from samples (Eq.2) from the same shared replay buffer, which contains all experiences collected from following different policies. We evaluate our proposed intrinsic reward SFC and the hierarchical framework of intrinsic motivation SID in three sets of simulated environments: VizDoom , DeepMind Lab and DeepMind Control Suite . Throughout all experiments, agents receive as input only raw pixels with no additional domain knowledge or task specific information. We mainly compare the following agent configurations: M: Ape-X DQN with 8 actors, train with only the extrinsic main task reward; ICM: train a single policy with the ICM reward bonus ; RND: train a single policy with the RND reward bonus (b); Ours: with our proposed SID framework, schedule between following the extrinsic main task policy and the intrinsic policy trained with our proposed SFC reward. We carried out an ablation study, where we compare the performance of an agent with intrinsic and extrinsic reward summed up, to the corresponding SID agent for each intrinsic reward type (ICM, RND, SFC). We present the plots and discussions in Section 4.4 Appendix A. For the intrinsic reward normalization and the scaling for the extrinsic and intrinsic rewards we do a parameter sweep for each environment (Appendix C.4) and choose the best setting for each agent. We notice that our scheduling agent is much less sensitive to different scalings than agents with added reward bonus. Since our proposed SID setup requires an off-policy algorithm to learn from experiences generated by following different policies, we implement all the agents under the Ape-X DQN framework. After a parameter sweep we set the number of scheduled tasks per episode to M = 8 for our agent in all experiments, meaning each episode is divided into up to 8 sub-episodes, and for each of which either the extrinsic or the intrinsic policy is sampled as the behavior policy. Appendix C and D contain additional information about experimental setups and model training details. We start by verifying our implementation of the baseline algorithms in "DoomMyWayHome" which was previously used in several state-of-the-art intrinsic motivation papers . The agent needs to navigate based only on first-person view visual inputs through 8 rooms connected by corridors (Fig.2a), each with a distinct texture (Fig.2c). The experimental are shown in Fig.3 (left). Since our basic RL algorithm is doing off-policy learning, it has relatively decent random exploration capabilities. We see that the M agent is able to solve the task sometimes without any intrinsically generated motivations, but that all intrinsic motivation types help to solve the task more reliably and speed up the learning. Our method solve the task the fastest, but also ICM and RND learn to reach the goal reliably and efficiently. We wanted to test the agents on a more difficult VizDoom map where structured exploration would be of vital importance. We thus designed a new map which scales up the navigation task of MyWayHome. Inspired by how flytraps catch insects, we design the layout of the rooms in a geometrically challenging way that escaping from one room to the next with random actions is extremely unlikely. We show the layout of MyWayHome (Fig.2a) and FlytrapEscape (Fig.2b) with the same downscaling ratio. The maze consists of 4 rooms separated by V-shaped walls pointing inwards the rooms. The small exits of each room is located at the junction of the V-shape, which is extremely difficult to maneuver into without a sequence of precise movements. As in the MyWayHome task, in each episode, the agent starts from the red dot shown in Fig.2b with a random orientation. An episode terminates if the final goal is reached and the agent will receive a reward of +1, or if a maximum episode steps of 10,000 (2100 for MyWayHome) is reached. The task is to escape the fourth room. The experimental on FlytrapEscape are shown in Fig.3 (right). Neither M nor RND manages to learn any useful policies. ICM solves the task in sometimes, while we can clearly observe that our method efficiently explores the map and reliably learns how to navigate to the goal. We visualize the learned successor features in Appendix E and its evolution over time is shown in the video https://gofile.io/?c=HpEwTd. In the second experiment, we set out to evaluate if the agents would be able to reliably collect the faraway big reward in the presence of small nearby distractive rewards. For this experiment we use the 3D visual navigation simulator of DeepMind Lab . We constructed a challenging level "AppleDistractions" (Fig.10b) with a maximum episode length of 1350. In this level, the agent starts in the middle of the map (blue square) and can follow either of the two corridors. Each corridor has multiple sections and each section consists of two dead-ends and an entry to next section. Each section has different randomly generated floor and wall textures. One of the corridors (left) gives a small reward of 0.05 for each apple collected, while the other one (right) contains a single big reward of 1 at the end of its last section. The optimal policy would be to go for the single faraway big reward. But since the small apple rewards are much closer to the spawning location of the agent, the challenge here is to still explore other areas sufficiently often so that the optimal solution could be recovered. The are presented in Fig.4 (left). Ours received on average the highest rewards and is the only method that learns to navigate to the large reward in every run. The baseline methods get easily distracted by the small short-term rewards and do not reliably learn to navigate away from the distractions. With a separate policy for intrinsic motivation the agent can for some time interval completely "forget" about the extrinsic reward and purely explore, since it does not get distracted by the easily reachable apple rewards and can efficiently learn to explore the whole map. In the meanwhile the extrinsic policy can simultaneously learn from the new experiences and might learn about the final goal discovered by the exploration policy. This highlights a big advantage of scheduling over bonus rewards, that it reduces the probability of converging to bad local optimums. In Section 4.4 we further showed that SID is generally applicable and also helps ICM and RND in this task. To show that our methods can be used in domains other than first-person visual navigation, we evaluate on the classic control task "cartpole: swingup sparse" , using third-person view images as inputs (Fig.11). The pole starts pointing down and the agent receives a single terminal reward of +1 for swinging up the unactuated pole using only horizontal forces on the cart. Additional details are presented in Appendix D.3. The are shown in Fig.4 (right). Compared to the previous tasks, this task is easy enough to be solved without intrinsic motivation, but we can see also that all intrinsic motivation methods significantly reduce the interaction time. Ours still outperforms other agents even in the absence of clear bottlenecks which shows its general applicability, but since the task is relatively less challenging for exploration, the performance gain is not as substantial as the previous experiments. Further, we conducted an ablation study on AppleDistractions. We denote with "M+SFC", "M+RND", "M+ICM" the agents with one policy where the respective intrinsic reward is added to the extrinsic one. With "SID(M,SFC)", "SID(M,RND)", "SID(M,ICM)" the agents are named that have two policies, one for the respective intrinsic and one for the extrinsic reward and use SID to schedule between them. We note that the "SID(M,ICM)" agent corresponds to the "Ours" agent from the previous experiments. The are presented in Figure 5. Our SID(M, SFC) agent received on average the highest rewards. Furthermore, we see that scheduling helped both ICM and SFC to find the goal and not settle for the small rewards, and SID also helps improve the performance of RND. The respective reward bonus counterparts of the three SID agents were more attracted to the small nearby rewards. This behavior is expected: By scheduling, the intrinsic policy of the SID agent is assigned with its own interaction time with the environment, during which it could completely "forget" about the extrinsic rewards. The agent then has a much higher probability of discovering the faraway big reward, thus escaping the distractions of the nearby small rewards. Once the intrinsic policy collects these experiences of the big reward, the extrinsic policy can immediately learn from those since both policies share the same replay buffer. Ablations for the other environments are reported in Appendix A. In this paper, we investigate an alternative way of utilizing intrinsic motivation for exploration in DRL. We propose a hierarchical agent SID that schedules between following extrinsic and intrinsic drives. Moreover, we propose a new type of intrinsic reward SFC that is general and evaluates the intrinsic motivation based on longer time horizons. We conduct experiments in three sets of environments and show that both our contributions SID and SFC help greatly in improving exploration efficiency. We consider many possible research directions that could stem from this work, including designing more efficient scheduling strategies, incorporating several intrinsic drives (that are possibly orthogonal and complementary) instead of only one into SID, testing our framework in other control domains such as manipulation, combining the successor representation with learned feature representations and extending our evaluation onto real robotics systems. We have conducted ablation studies for all the three sets of environments to investigate the influence of scheduling on our proposed method, whether other reward types can benefit from scheduling too, and whether environment specific differences exist. We compare the performance of the following agent configurations: • Three reward bonus agents M+ICM, M+RND, M+SFC: The agent receives the intrinsic reward of ICM , RND (b) or our proposed SFC respectively as added bonus to the extrinsic main task reward and trains a mixture policy on this combined reward signal. We note that the M+ICM and M+RND agent in this section corresponds to the ICM and RND agent in all other sections respectively. The agent schedules between following the extrinsic main task policy and the intrinsic policy trained with the ICM, RND or our proposed SFC reward respectively. We note that the SID (M, SFC) agent in this section corresponds to the Ours agent in all other sections. The on AppleDistractions were shown in in Section 4.4 the main paper. In Fig.6 (left), we present the ablation study for FlytrapEscape. The agents with the ICM component perform poorly. Only 1 run of M+ICM learned to navigate to the goal, while the scheduling agent SID(M,ICM) did not solve the task even once. But for the two SFC agents, the scheduling greatly improves the performance. Although the reward bonus agent M+SFC was not successful in every run, the SID(M,SFC) agent solved the FlytrapEscape in 5 out of 5 runs. We hypothesize the reason for the superior performance of SID(M,SFC) compared to M+SFC could be the following: Before seeing the final goal for the first time, the M+SFC agent is essentially learning purely on the SFC reward, which is equivalent to the intrinsic policy of the scheduling SID(M,SFC) agent. Since SFC might preferably go to bottleneck states as the difference between the SF of the two neighboring states are expected to be relatively larger for those states. Since the extrinsic policy is doing random exploration before receiving any reward signal, it could be a good candidate to explore the next new room from the current bottleneck state onwards. Then the SFs of the new room will be learned when it is being explored, which would then guide the agent to the next bottleneck regions. Thus the SID(M,SFC) agent could efficiently explore from bottleneck to bottleneck, while the M+SFC agent could not be able to benefit from the two different behaviors under the extrinsic and intrinsic rewards and could oscillate around bottleneck states. On the other hand, scheduling did not help ICM or RND. A reason could be that ICM or RND is not especially attracted by bottleneck states so it does not help exploration if the agent spends half of the time acting randomly as the extrinsic policy had no reward yet to learn from. Also since the FlytrapEscape environment is extremely explorationchallenging, the temporally extended view of our proposed SFC might of vital importance to guide efficient exploration. In Fig.6 (right), we present the ablation study for Cartpole. We can observe that SID helps to improve the performance of both ICM and RND. As for SFC, although the reward bonus agent learns a bit faster than the SID agent, we note that actually all the three SID agent converge to more stable policies, while the reward bonus agents tend to oscillate around the optimal return. In experiments of the main paper with SID the scheduler chooses 8 times per episode which policy to follow until a new policy is chosen. We conducted a further experiment to examine how different numbers of switches per episode affects the performance of the agent. We carried out the experiment on "DoomMyWayHome" with an agent using SID with SFC for the intrinsic reward. The are show in 7 C APPENDIX: IMPLEMENTATION DETAILS This section describes implementation details and design choices. The backbone of our algorithm implementation is presented in Section 3.4 and visualized in Fig. 8. Since our algorithm requires an off-policy learning strategy, and in consideration for faster learning and less computation overhead, we use the state-of-the-art off-policy algorithm with the K-step target (K = 5) for bootstraping without off-policy correction where θ − denotes the target network parameters. We chose the number of actors the be the highest the hardware supported, which was 8. To adapt the settings from the 360 actors in the Ape-X DQN to our setting of N = 8 actors, we set a fixed i for each actor i ∈ {1, . . ., 8} as i = where α = 7 and = 0.4 are set as in the original work. For computational efficiency, we implement our own version of the prioritized experience replay. We split the replay buffer into two, with size of 40, 000 and 10, 000. Every transition is pushed to the first one, while in the second one only transitions are pushed on which a very large TD-error is computed. We store a running estimate of the mean and the standard deviation of the TD-errors and if for a transition the error is larger than the mean plus two times the standard deviation, the transition is pushed. In the learner a batch of size 128 consists of 96 transitions drawn from the normal replay buffer and 32 are drawn from the one that stores transition with high TD-error, which as a have relatively seen a higher chance of being picked. We note that previous works for learning the deep SF have included an auxiliary task of reconstruction on the features φ Kulkarni et al. (2016a); , while in this work we investigate learning ψ without this extra reconstruction stream. Instead of adapting the features φ while learning the successor features ψ, we fix the randomly initialized φ. This design follows the intuition that since SF (ψ) estimates the expectation of features (φ) under the transition dynamics and the policy being followed, more stable learning of the SF could be achieved if the features are kept fixed. The SF are learned from the same replay buffer as for training the Q-Net. Since our base algorithm is K-step Ape-X, and we follow the memory efficient implementation of the replay buffer as suggested in Ape-X, we only have access to K-step experience tuples (K = 5) for learning the SF. Therefore we calculate the intrinsic reward by applying the canonical extension of the SFC reward formulation (Eq.4) to K-step transitions The behaviour policy π associated with the SF is not given explicitly, but since the SF are learned from the replay buffer via TD learning, it is a mixture of current and past behaviour policies from all actors. Most network parameters are shared for estimating the expected discounted return of the intrinsic and extrinsic rewards. The scale of the rewards has a big influence on the scale of the gradients for the network parameters. Hence, it is important that the rewards are roughly on the same scale, otherwise effectively different learning rates are applied. The loss of the network comes from the regression on the Q-values, which approximate the expected return. So our normalization method aims to bring the discounted return of both tasks into the same range. To do so we first normalize the intrinsic rewards by dividing them by a running estimate of their standard deviation. We also keep a running estimate of the mean of this normalized reward and denote it r I. Since every time step an intrinsic reward is received we estimate the discounted return via the geometric series. We scale the extrinsic task reward that is always in {0, 1} with η, where γ I is the discount rate for the intrinsic reward. Furthermore, η is a hyperparameter which takes into account that for Q-values from states more distant to the goal the reward is discounted with the discount rate for the extrinsic reward depending on how far away that state is. In our experiments we set η = 3. We did the same search for hyperparameters and normalization technique for all algorithms that include an intrinsic reward and found out that the procedure above works best for all of them. The algorithms were evaluated on the FlytrapEscape. For η we tried the values in {0.3, 1, 3, 10}. We also tried to not normalize the rewards and just scale the intrinsic reward. To scale the intrinsic reward we tried the values {0.001, 0.01, 0.1, 1}. However, we found that as the scale of the intrinsic rewards is not the same over the whole training process this approach does not work well. We also tried to normalize the intrinsic rewards by dividing it by a running estimate of its standard deviation and then scale this quantity with a value in {0.01, 0.1, 1}. We use the same model architecture as depicted in Fig. 9 across all 3 sets of experiments. ReLU activations are added after every layer except for the last layers of each dashed blocks in the above figure. For the experiments with the ICM , we added BatchNorm before activation for the embedding of the ICM module following the original code released by the authors. Code is implemented in pytorch . For all experiments we used a stack of 4 consecutive, preprocessed observations as states. For the first-person view experiments in VizDoom and DeepMind Lab, we use an action repetition of 4, while for the classic control experiment we did not apply action repetition. In the text, we only refer to the actual environment steps (e.g. before divided by 4). The VizDoom environment produces 320 × 240 RGB images as observations. In a preprocessing step, we downscaled the images to 84 × 84 pixels and converted them to grayscale. For FlytrapEscape, we adopted the action space settings from the MyWayHome task. The action space was given by the following 5 actions: TURN LEFT, TURN RIGHT, MOVE FORWARD, MOVE LEFT, MOVE RIGHT We setup the DmLab environment to produce 84 × 84 RGB images as observations. In Fig.10 we show examplary observations of AppleDistractions. We preprocessed the images by converting the observations to grayscale. For a given enviroment seed, textures for each segment of the maze are generated at random. We used the predefined DmLab actions from. The action space was given by the following 8 actions (no shooting setting): Forward, Backward, Strafe Left, Strafe Right, Look Left, Look Right, Forward+Look Left, Forward+Look Right. We conducted the experiments for the classic control task on the'Cart-pole' domain with the'swingup sparse' task provided by the DeepMind Control Suite. Since our agents needs a discrete action space and the control suite only provides continuous action spaces, we discretized the single action dimension. The set of actions was {-0.5, -0.25, 0, 0.25, 0.5}. We configured the environment to produce 84×84 RGB pixel-only observations from the 1st camera, which is the only predefined camera that shows the full cart and pole at all times. We further convert the images to grey-scale and stack four consecutive frames as input to our network. The episode length was 200 environment steps. In the four-room domain, the agent can transition to directly connected states using the four actions'up','down','left' and'right'. For Fig.1 a),b) the successor features were calculated analytically via the formula Ψ = (I − γP) − 1, where P denotes the one-step transition matrix. The SF discount factor was set to γ = 0.95. For Fig.1 c),d) the agents performed 10000 episodes with 30 steps each. These short episodes ensure that exploration remains challenging, even in a relatively small environment. In d), the learning rate for the SF as well as the Q-table was set to 0.05. To prevent optimistic initialization effects the Q-table was initialized to 0. To generate our we used two machines that run Ubuntu 16.04. Each machine has 4 GeForce Titan X (Pascal) GPUs. On one machine we run 4 experiments in parallel, each experiment on a separate GPU. E APPENDIX: SUCCESSOR DISTANCE VISUALIZATION Figure 12: Projection of the SFs. For the purpose of visualization we discretized the map into 85 × 330 grids and position the trained agent SID(M,SFC) at each grid, then computed the successor features ψ for that location for each of the 4 orientations (0°, 90°, 180°, 270°), which ed in a 4 × 512 matrix. We then calculated the l2-difference of this matrix with a 4 × 512 vector containing the successor features of the starting position with the 4 different orientations. Shown in log-scale. As an additional evaluation, we visualize the SF of an Ours agent (i.e. trained with SID which schedules between the extrinsic policy and the SFC policy) at the end of the training (Fig.12). That means the SF are trained with the experiences from the behaviour policy of our agent. We can see that the SD from each coordinate to the starting position tends to grow as the geometric distance increases, especially for those that locate on the pathways leading to later rooms. This shows that the learned SD and the geometric distance are in good agreement and that the SF are learned as expected. Furthermore, we observe big intensity changes around the bottlenecks (the room entries) in the heatmap, which also supports the hypothesis that SFC leads the agent to bottleneck states. We believe this is the first time that SF are shown to behave in a first-person view environment as one would expect from its definition. The evolution of the SF over time is shown in the video https://gofile.io/?c=HpEwTd. When learning optimal value functions or optimal policies via TD or policy gradient with deep function approximators, optimizing with algorithms such as gradient descent means that the policy would only evolve incrementally: It is necessary that the TD-target values do not change drastically over a short period of time in order for the gradient updates to be meaningful. The common practice of utilizing a target network in off-policy DRL stabilizes the update but in the meanwhile making the policy adapt even more incrementally over each step. But intrinsically motivated exploration, or exploration in general, might benefit from an opposite treatment of the policy update. This is because the intrinsic reward is non-stationary by nature, as well as the fact that the exploration policy should reflect the optimal strategy corresponding to the current stage of learning, and thus is also non-stationary. With the commonly adopted way of using intrinsic reward as a bonus to the extrinsic reward and train a mixture policy on top, exploration would be a balancing act between the incrementally updated target values for stable learning and the dynamically adapted intrinsic signals for efficient exploration. Moreover, neither the extrinsic nor the intrinsic signal is followed for an extended amout of time. Therefore, we propose to address this issue with a hierarchical approach that by design has slowly changing target values while still allowing drastic behavior changes. The idea is to learn not a single, but multiple policies, with each one optimizing on a different reward function. To be more specific, we assume to have N tasks T ∈ T (e.g. N = 2 and T = {T E, T I} where T E denotes the extrinsic task and T I the intrinsic task) defined by N reward functions (e.g. R E and R I) that share the state and action space. The optimal policy for each of these N different MDPs can be learned with arbitrary off-policy DRL algorithms. During each episode, a high-level scheduler periodically selects a policy for the agent to follow to gather experiences, and each policy is trained with all experiences collected following those N different policies. The overall learning objective is to maximize the extrinsic reward E ω(T|St) E π T (At|St) [q T E (S t, A t |A t ∼ π T (·|S t))] (ω: the macro-policy of the scheduler). By allowing the agent to follow one motivation at a time, it is possible to have a pool of N different behavior policies without creating unstable targets for off-policy learning. By scheduling M times even during an episode, we implicitly increase the behavior policy space by exponential to N M for a single episode. Moreover, disentangling the extrinsic and intrinsic policy strictly separates stationary and non-stationary behaviors, and the different sub-objectives would each be allocated with its own interaction time, such that extrinsic reward maximization and exploration do not distract each other. We investigated several types of high-level schedulers, however, none of them consistently outperforms a random one. We suspect the reason why a random scheduler already performs very well under the SID framework, is that a highly stochastic schedule can be beneficial to make full use of the big behavior policy space. We investigated three types of high-level schedulers: • Random scheduler: Sample a task from uniform distribution every task steps. • Switching scheduler: Sequentially switches between extrinsic and intrinsic task. • Macro-Q Scheduler: Learn a scheduler that learns with macro actions and from subsampled experience tuples. In each actor, we keep an additional local buffer that stores N + 1 subsampled experiences: {s t−N m, . . ., s t−2m, s t−m, s t}. Then at each environment step, Besides the K-step experience tuple mentioned above, we also store an additional macro-transition {s t−N m, s t} along with its sum of discounted rewards to the shared replay buffer. This macro-transition is paired with the current task as its macro-action. The Macro-Q Scheduler is then learned with an additional output head attached to θ ϕ (we also tried θ φ). • Threshold-Q Scheduler: Selects task according to the Q-value output of the extrinsic task head. For this scheduler no additional learning is needed. It just selects a task based on the current Q-value of the extrinsic head θ e. We tried the following selection strategies: -Running mean: select intrinsic when the current Q-value of the extrinsic head is below its running mean, extrinsic otherwise -Heuristic median: observing that the running mean of the Q-values might not be a good statistics for selecting tasks due to the very unevenly distributed Q-values across the map, we choose a fixed value that is around the median of the Q-values (0.007), and choose intrinsic when below, extrinsic otherwise As we report in the paper, none of the above scheduler choices consistently performs better across all environments than a random scheduler. We leave this part to future work. G APPENDIX: SINGLE RUNS

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A new intrinsic reward signal based on successor features and a novel way to combine extrinsic and intrinsic reward.

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Adaptation of an RL agent in a target environment with unknown dynamics is fast and safe when we transfer prior experience in a variety of environments and then select risk-averse actions during adaptation.


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Question: Meta-Reinforcement learning approaches aim to develop learning procedures that can adapt quickly to a distribution of tasks with the help of a few examples. Developing efficient exploration strategies capable of finding the most useful samples becomes critical in such settings. Existing approaches to finding efficient exploration strategies add auxiliary objectives to promote exploration by the pre-update policy, however, this makes the adaptation using a few gradient steps difficult as the pre-update (exploration) and post-update (exploitation) policies are quite different. Instead, we propose to explicitly model a separate exploration policy for the task distribution. Having two different policies gives more flexibility in training the exploration policy and also makes adaptation to any specific task easier. We show that using self-supervised or supervised learning objectives for adaptation stabilizes the training process and also demonstrate the superior performance of our model compared to prior works in this domain. Reinforcement learning (RL) approaches have seen many successes in recent years, from mastering the complex game of Go BID10 to even discovering molecules BID8. However, a common limitation of these methods is their propensity to overfitting on a single task and inability to adapt to even slightly perturbed configuration BID12. On the other hand, humans have this astonishing ability to learn new tasks in a matter of minutes by using their prior knowledge and understanding of the underlying task mechanics. Drawing inspiration from human behaviors, researchers have proposed to incorporate multiple inductive biases and heuristics to help the models learn quickly and generalize to unseen scenarios. However, despite a lot of effort it has been difficult to approach human levels of data efficiency and generalization. Meta-RL tries to address these shortcomings by learning these inductive biases and heuristics from the data itself. These inductive biases or heuristics can be induced in the model in various ways like optimization, policy initialization, loss function, exploration strategies, etc. Recently, a class of policy initialization based meta-learning approaches have gained attention like Model Agnostic MetaLearning (MAML) BID1. MAML finds a good initialization for a policy that can be adapted to a new task by fine-tuning with policy gradient updates from a few samples of that task. Given the objective of meta RL algorithms to adapt to a new task from a few examples, efficient exploration strategies are crucial for quickly finding the optimal policy in a new environment. Some recent works BID3 have tried to address this problem by using latent variables to model the distribution of exploration behaviors. Another set of approaches BID11 BID9 focus on improving the credit assignment of the meta learning objective to the pre-update trajectory distribution. However, all these prior works use one or few policy gradient updates to transition from preto post-update policy. This limits the applicability of these methods to cases where the post-update (exploitation) policy is similar to the pre-update (exploration) policy and can be obtained with only a few updates. Also, for cases where pre-and post-update policies are expected to exhibit different behaviors, large gradient updates may in training instabilities and lack of convergence. To address this problem, we propose to explicitly model a separate exploration policy for the distribution of tasks. The exploration policy is trained to find trajectories that can lead to fast adaptation of the exploitation policy on the given task. This formulation provides much more flexibility in training the exploration policy. In the process, we also establish that, in order to adapt as quickly as possible to the new task, it is often more useful to use self-supervised or supervised learning approaches, where possible, to get more effective updates. Unlike RL which tries to find an optimal policy for a single task, meta-RL aims to learn a policy that can generalize to a distribution of tasks. Each task T sampled from the distribution ρ(T) corresponds to a different Markov Decision Process (MDP). These MDPs have similar state and action space but might differ in the reward function or the environment dynamics. The goal of meta RL is to quickly adapt the policy to any task T ∼ ρ(T) with the help of few examples from that task. BID1 introduced MAML -a gradient-based meta-RL algorithm that tries to find a good initialization for a policy which can be adapted to any task T ∼ ρ(T) by fine-tuning with one or more gradient updates using the sampled trajectories of that task. MAML maximizes the following objective function: where U is the update function that performs one policy gradient ascent step to maximize the expected reward R(τ) obtained on the trajectories τ sampled from task T. BID9 showed that the gradient of the objective function J(θ) can be written as: DISPLAYFORM0 where, ∇ θ J post (τ, τ) optimizes θ to increase the likelihood of the trajectories τ that lead to higher returns given some trajectories τ. In other words, this term does not optimize θ to yield trajectories τ that lead to good adaptation steps. That is infact, done by the second term ∇ θ J pre (τ, τ). It optimizes for the pre-update trajectory distribution, P T (τ |θ), i.e, increases the likelihood of trajectories τ that lead to good adaptation steps. During optimization, MAML only considers J post (τ, τ) and ignores J pre (τ, τ). Thus MAML finds a policy that adapts quickly to a task given relevant experiences, however, the policy is not optimized to gather useful experiences from the environment that can lead to fast adaptation. ProMP BID9 analyzes this issue with MAML and incorporates ∇ θ J pre (τ, τ) term in the update as well. They propose to use DICE BID2 to allow causal credit assignment on the pre-update trajectory distribution, however, the gradients computed by DICE suffer from high variance estimates. To remedy this, they proposed a low variance (and slightly biased) approximation of the DICE based loss that leads to stable updates. The pre-update and post-update policies are often expected to exhibit very different behaviors, i.e, exploration and exploitation behaviors respectively. In such cases, transitioning a single policy from pure exploration phase to pure exploitation phase via policy gradient updates will require multiple steps. Unfortunately, this significantly increases the computational and memory complexities of the algorithm. Furthermore, it may not even be possible to achieve this transition via few gradient updates. This raises an important question: DO WE REALLY NEED TO USE THE PRE- Using separate policies for pre-update and post-update sampling: The straightforward solution to the above problem is to use a separate exploration policy µ φ responsible for collecting trajectories for the inner loop updates to get θ. Following that, the post-update policy π θ can be used to collect trajectories for performing the outer loop updates. Unfortunately, this is not as simple as it sounds. To understand this, let's look at the inner loop updates: DISPLAYFORM0 When using the exploration policy for sampling, we need to perform importance sampling. The update thus becomes: DISPLAYFORM1 where P T (τ |θ) and Q T (τ |φ) represent the trajectory distribution sampled by π θ and µ φ respectively. Note that the above update is an off-policy update which in high variance estimates when the two trajectory distributions are quite different from each other. This makes it infeasible to use the importance sampling update in the current form. In fact, this is a more general problem that arises even in the on-policy regime. The policy gradient updates in the inner loop in both ∇ θ J pre and ∇ θ J post terms being high variance. This stems from the mis-alignment of the outer gradients (∇ θ J outer) and the inner gradient,hessian Using a self-supervised/supervised objective for the inner loop update step: The instability in the inner loop updates arises due to the high variance nature of the policy gradient update. Note that the objective of inner loop update is to provide some task specific information to the agent with the help of which it can adapt its behavior in the new environment. We believe that this could be achieved using some form of self-supervised or supervised learning objective in place of policy gradient in the inner loop to ensure that the updates are more stable. We propose to use a network for predicting some task (or MDP) specific property like reward function, expected return or value. During the inner loop update, the network updates its parameters by minimizing its prediction error on the given task. Unlike prior meta-RL works where the task adaptation in the inner loop is done by policy gradient updates, here, we update some parameters shared with the exploitation policy using a supervised loss objective function ing in stability during the adaptation phase. However, note that the variance and usefulness of the update depends heavily on the choice of the self-supervision/supervision objective. We delve into this in more detail in the appendix. DISPLAYFORM2 Our proposed model comprises of three modules, the exploration policy µ φ (s), the exploitation policy π θ,z (s), and the self-supervision network M β,z (s, a). Note that M β,z and π θ,z share a set of parameters z while containing their own set of parameters β and θ respectively. The agent first collects a set of trajectories τ using its exploration policy µ φ for each task T ∼ ρ(T). It then updates the shared parameter z by minimizing the regression DISPLAYFORM0 where, M (s, a) is the target which can be any of the task specific quantities as mentioned above. We further modify the above equation by multiplying the DICE operator to simplify the gradient computation w.r.t φ. This eliminates the need to apply the policy gradient trick to expand the above expression for gradient computation. The update then becomes: DISPLAYFORM1 where ⊥ is the stop gradient operator. After obtaining the updated parameters z, the agent samples trajectories τ using its updated exploitation policy π θ,z. Note that our model enables the agent to learn a generic exploitation policy π θ,z for the task distribution which can then be adapted to any specific task by updating z to z as shown above. Effectively, z encodes the necessary information regarding the task that helps an agent in adapting its behavior to maximize its expected return. The collected trajectories are then used to perform a policy gradient update for all the parameters z, θ, φ and β using the following objective: DISPLAYFORM2 The gradients of J(z, θ) w.r.t. φ are shown in Eq. 6 (see appendix). Although the gradients are unbiased, they still have very high variance. To solve this problem, we draw inspiration from BID7 and replace the return R µ t (see Eq. 7 in appendix) with an advantage estimate A µ t (see 8 in appendix). Due to space constraints we describe these formulations in more detail in appendix. We have evaluated our proposed model on the environments used by BID9. Specifically, we have used HalfCheetahFwdBack, HalfCheetahVel and Walker2DFwdBack environments for the dense reward tasks and a 2D point environment proposed in BID9 for sparse rewards. The details of the network architecture and the hyperparameters used for learning have been mentioned in the appendix. We would like to state that we have not performed much hyperparameter tuning due to computational constraints and we expect the of our method to show further improvements with further tuning. Also, we restrict ourselves to a single adaptation step in all environments for the baselines as well as our method, but it can be easily extended to multiple gradient steps as well by conditioning the exploration policy on z. The of the baselines for the benchmark environments have been borrowed directly from the the official ProMP website 1. For the point environments, we have used the publicly available official implementation 2. We also compare our method with 3 baseline approaches: MAML, EMAML and ProMP on the benchmark continuous control tasks. The performance plots for all four algorithms are shown in FIG0. In all the environments, our proposed method outperforms others in terms of asymptotic performance. The training is also more stable for our method and leads to lower variance plots. Our algorithm particularly shines in 2DPointEnvCorner FIG1 where the reward is sparse. In this environment, the agent needs to perform efficient exploration and use the sparse reward trajectories to perform stable updates both of which are salient aspects of our algorithm. Although ProMP manages to reach similar peak performance to our method in 2DPointEnvCorner, the training itself is pretty unstable indicating the inherent fragility of their updates. Further, we show that our method leads to good exploration behavior in a sparse reward point environment where the agent is allowed to sample only two trajectories in order to perform the updates illustrating the strength of our procedure. We also show that the separation of exploration and exploitation policies in this scenario allows us to train the exploration policy using an independent objective providing better performance in certain situations. Ablations: We perform several ablation experiments to analyze the impact of different components of our algorithm on 2D point navigation task. FIG1 shows the performance plots for 5 different variants: VPG-Inner loop: The supervised loss in the inner loop is replaced with the vanilla policy gradient loss as in MAML while using the exploration policy to sample the pre-update trajectories. As expected, this model performs poorly due to the high variance off-policy updates in the inner loop. Reward Self-Supervision: A reward based self-supervised objective is used instead of return based self-supervision. This variant performs reasonably well but struggles to reach peak performance since the task is sparse reward. Vanilla DICE: We directly use the dice gradients to perform updates on φ instead of using the low variance gradient estimator. The high variance dice gradients lead to unstable training as can be seen from the plots. E-MAML Based: Used an E-MAML BID11 type objective to compute the gradients w.r.t φ instead of using DICE. Although this variant manages to reach peak performance, it is unstable due to the lack of causal credit assignment. Ours: Used the low variance estimate of the dice gradients to compute updates for φ along with return based self-supervision for inner loop updates. Our model reaches peak performance and exhibits stable training due to low variance updates. Unlike conventional meta-RL approaches, we proposed to explicitly model a separate exploration policy for the task distribution. Having two different policies gives more flexibility in training the exploration policy and also makes adaptation to any specific task easier. Hence, as future work, we would like to explore the use of separate exploration and exploitation policies in other meta-learning approaches as well. We showed that, through various experiments on both sparse and dense reward tasks, our model outperforms previous works while also being very stable during training. This validates that using self-supervised techniques increases the stability of these updates thus allowing us to use a separate exploration policy to collect the initial trajectories. Further, we also show that the variance reduction techniques used in the objective of exploration policy also have a huge impact on the performance. However, we would like to note that the idea of using a separate exploration and exploitation policy is much more general and doesn't need to be restricted to MAML. that to compute M β,z (s t, a t) = w T β m β (s t, a t). Using the successor representations can effectively be seen as using a more accurate/powerful baseline than directly predicting the N-step returns using the (s t, a t)pair. We perform some additional experiments on another toy environment to illustrate the exploration behavior shown by our model and demonstrate the benefits of using different exploration and exploitation policies. FIG2 an environment where the agent is initialized at the center of the semi-circle. Each task in this environment corresponds to reaching a goal location (red dot) randomly sampled from the semi circle (green dots). This is also a sparse reward task where the agent receives a reward only if it is sufficiently close to the goal location. However, unlike the previous environments, we only allow the agent to sample 2 pre-update trajectories per task in order to identify the goal location. Thus the agent has to explore efficiently at each exploration step in order to perform reasonably at the task. FIG2 the trajectories taken by our exploration agent (orange and blue) and the exploitation/trained agent (green). Clearly, our agent has learnt to explore the environment. However, we know that a policy going around the periphery of the semi-circle would be a more useful exploration policy. In this environment we know that this exploration behavior can be reached by simply maximizing the environment rewards collected by the exploration policy. FIG3 shows this experiment where the exploration policy is trained using environment reward maximization while everything else is kept unchanged. We call this variant Ours-EnvReward. We also show the trajectories traversed by promp in FIG4 It is clear that it struggles to learn different exploration and exploitation behaviors. FIG5 shows the performance of our two variants along with the baselines. This experiment shows that decoupling the exploration and exploitation policies also allows us, the designers more flexibility at training them, i.e, it allows us to add any domain knowledge we might have regarding the exploration or the exploitation policies to further improve the performance. We also experiment with Walker2DRandParams and HopperRandParams. The different tasks in these environments arise from variations in the dynamics of the agent. The are shown in FIG7 We observe that in both these environments we match the performance of the baselines but don't really perform much better. This could be because we still use the n-step return as the self-supervision objective in our experiments. We expect the to get better if we test with next-state prediction etc as self-superivision objectives. We leave that for future work. For all the experiments, we treat the shared parameter z as a learnable latent embedding with fixed initial values of 0 as proposed in BID13,i.e, we don't perform any outer-loop updates on z.. The exploitation policy π θ,z (s) and the self-supervision network M β,z (s, a) concatenates z with their respective inputs. All the three networks (π, µ, M) have the same architecture (except inputs and output sizes) as that of the policy network in BID9 for all experiments. We also stick to the same values of hyper-parameters such as inner loop learning rate, gamma, tau and number of outer loop updates. We keep a constant embedding size of 32 and a constant N=15 (for computing the N-step returns) across all experiments and runs. We use the Adam BID5 optimizer with a learning rate of 7e − 4 for all parameters except φ, which uses a learning rate of 7e − 5. Also, we restrict ourselves to a single adaptation step in all environments, but it can be easily extended to multiple gradient steps as well by conditioning the exploration policy on the latent parameters z. We have provided a version of our code in the supplementary material. We will soon open source a cleaned version of this online.

We propose to use a separate exploration policy to collect the pre-adaptation trajectories in MAML. We also show that using a self-supervised objective in the inner loop leads to more stable training and much better performance.

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We augment the Q-value estimates with a count-based bonus that ensures optimism during action selection and bootstrapping, even if the Q-value estimates are pessimistic.


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Question: The “Supersymmetric Artificial Neural Network” in deep learning (denoted (x; θ, bar{θ})Tw), espouses the importance of considering biological constraints in the aim of further generalizing backward propagation. Looking at the progression of ‘solution geometries’; going from SO(n) representation (such as Perceptron like models) to SU(n) representation (such as UnitaryRNNs) has guaranteed richer and richer representations in weight space of the artificial neural network, and hence better and better hypotheses were generatable. The Supersymmetric Artificial Neural Network explores a natural step forward, namely SU(m|n) representation. These supersymmetric biological brain representations (Perez et al.) can be represented by supercharge compatible special unitary notation SU(m|n), or (x; θ, bar{θ})Tw parameterized by θ, bar{θ}, which are supersymmetric directions, unlike θ seen in the typical non-supersymmetric deep learning model. Notably, Supersymmetric values can encode or represent more information than the typical deep learning model, in terms of “partner potential” signals for example. Introduction. Machine learning non-trivially concerns the application of families of functions that guarantee more and more variations in weight space. This means that machine learning researchers study what functions are best to transform the weights of the artificial neural network, such that the weights learn to represent good values for which correct hypotheses or guesses can be produced by the artificial neural network. The "Supersymmetric Artificial Neural Network" (or 'thought curvature') is reasonably yet another way to represent richer values in the weights of the model; because supersymmetric values can allow for more information to be captured about the input space. For example, supersymmetric systems can capture potential-partner signals, which is beyond the feature space of magnitude and phase signals learnt in typical real valued neural nets and deep complex neural networks respectively. As such, a brief historical progression of geometric solution spaces for varying neural network architectures follows:1. An optimal weight space produced by shallow or low dimension integer valued nodes or real valued artificial neural nets, may have good weights that lie for example, in one simple (ℤ ℝ −) cone per class/target group. (This may guarantee some variation, but not enough for more sophisticated tasks of higher dimension) BID42. An optimal weight space produced by deep and high-dimension-absorbing real valued artificial neural nets, may have good weights that lie in disentangleable (ℝ * ℝ −) manifolds per class/target group convolved by the operator *, instead of the simpler regions per class/target group seen in item. parameterized by,, which are supersymmetric directions, unlike seen in the typical nonsupersymmetric deep learning model. Notably, Supersymmetric values can encode or represent more information than the typical deep learning model, in terms of "partner potential" signals for example. This paper does not contain empirical code concerning supersymmetric artificial neural networks, although it does highlight empirical evidence, that indicates how such types of supersymmetric learning models could exceed the state of the art, due to preservation features seen in progressing through earlier related models from the days of older perceptron like models that were not supersymmetric.(This may guarantee more variation in the weight space than, leading to better hypotheses or guesses) BID5 3. An optimal weight space produced by shallow but high dimension-absorbing complex valued artificial neural nets, may have good weights that lie in multiple (ℂ −) sectors per class/target group, instead of the real regions per class/target group seen amongst the prior items. (This may guarantee more variation of the weight space than the previous items, by learning additional features, in the "phase space". This also leads to better hypotheses/guesses) BID6 4. An optimal weight space produced by deep or high dimension-absorbing complex valued artificial neural nets, may have good weights that lie in chi distribution bound, (ℂ * ℂ −) rayleigh space per class/target group convolved by the operator *, instead of the simpler sectors/regions per class/target group seen amongst the previous items. (This may guarantee more variation of the weight space than the prior items, by learning phase space representations, and by extension, strengthen these representations via convolutional residual blocks. This also leads to better hypotheses/guesses) BID7 5. The "Supersymmetric Artificial Neural Network" operable on high dimensional data, may reasonably generate good weights that lie in disentangleable (∞ ( |) − ) supermanifolds per class/target group, instead of the solution geometries seen in the prior items above. Supersymmetric values can encode rich partner-potential delimited features beyond the phase space of in accordance with cognitive biological space BID2, where lacks the partner potential formulation describable in Supersymmetric embedding. BID8 Another view of "solution geometry" history, which may promote a clear way to view the reasoning behind the subsequent pseudocode sequence.1. There has been a clear progression of "solution geometries", ranging from those of the ancient Perceptron BID4 to complex valued neural nets BID7, grassmann manifold artificial neural networks BID11 or unitaryRNNs. BID10 BID14 These models may be denoted by ⊤ parameterized by, expressible as geometrical groups ranging from orthogonal BID3 to special unitary group BID16 based: to …, and they got better at representing input data i.e. representing richer weights, thus the learning models generated better hypotheses or guesses. 2. By "solution geometry" I mean simply the class of regions where an algorithm's weights may lie, when generating those weights to do some task. 3. As such, if one follows cognitive science, one would know that biological brains may be measured in terms of supersymmetric operations. (Perez et al, "Supersymmetry at brain scale" BID2) 4. These supersymmetric biological brain representations can be represented by supercharge BID9 compatible special unitary notation (|), or (;,) ⊤ parameterized by, BID8, which are supersymmetric directions, unlike seen in item BID0. Notably, Supersymmetric values can encode or represent more information than the prior classes seen in, in terms of "partner potential" signals for example. 5. So, state of the art machine learning work forming or based solution geometries, although nonsupersymmetric, are already in the family of supersymmetric solution geometries that may be observed as occurring in biological brain or (|) supergroup BID15 representation. A naive supersymmetric artificial neural network architecture. (See points 1 to 5 in BID13) It seems feasible that a C ∞ bound atlas-based learning model, where said C ∞ is in the family of supermanifolds from supersymmetry, may be obtained from a system, which includes charts of grassmann manifold networks, and stiefel manifolds,, in (,) terms, where there exists some invertible submatrix entailing matrix ∈ (∩) for = where is a submersion mapping on some stiefel manifold,, thereafter enabling some differentiable grassmann manifold (ℝ) wherein = {∈ ℝ × : ≠ 0}. Pertinently, the "Edward Witten/String theory powered supersymmetric artificial neural network", is one wherein supersymmetric weights are sought. Many machine learning algorithms are not empirically shown to be exactly biologically plausible, i.e. Deep Neural Network algorithms, have not been observed to occur in the brain, but regardless, such algorithms work in practice in machine learning. Likewise, regardless of Supersymmetry's elusiveness at the LHC, as seen above, it may be quite feasible to borrow formal methods from strategies in physics even if such strategies are yet to show related physical phenomena to exist; thus it may be pertinent/feasible to try to construct a model that learns supersymmetric weights, as I proposed throughout this paper, following the progression of solution geometries going from to and onwards to (|) BID15.

Generalizing backward propagation, using formal methods from supersymmetry.

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We show that neural networks operate by changing topologly of a data set and explore how architectural choices effect this change.