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Online Bayesian Moment Matching based SAT Solver Heuristics | null | In this paper, we present a Bayesian Moment Matching (BMM) based method aimed at solving the initialization problem in Boolean SAT solvers. The initialization problem can be stated as follows: given a SAT formula $\phi$, compute an initial order over the variables of $\phi$ and values/polarity for these variables such that the runtime of SAT solvers on input $\phi$ is minimized. At the start of a solver run, our BMM-based methods compute a posterior probability distribution for an assignment to the variables of the input formula after analyzing its clauses, which will then be used by the solver to initialize its search. We perform extensive experiments to evaluate the efficacy of our BMM-based heuristic against 4 other initialization methods (random, survey propagation, Jeroslow-Wang, and default) in state-of-the-art solvers, MapleCOMSPS and MapleLCMDistChronotBT over the SAT competition 2018 application benchmark, as well as the best-known solvers in the cryptographic category, namely, CryptoMiniSAT, Glucose, and MapleSAT. On the cryptographic benchmark, BMM-based solvers out-perform all other initialization methods. Further, the BMM-based MapleCOMSPS significantly out-perform the same solver using all other initialization methods by 12 additional instances solved and better average runtime, over the SAT 2018 competition benchmark. | Haonan Duan, Saeed Nejati, George Trimponias, Pascal Poupart, Vijay Ganesh | null | null | 2,020 | icml |
Familywise Error Rate Control by Interactive Unmasking | null | We propose a method for multiple hypothesis testing with familywise error rate (FWER) control, called the i-FWER test. Most testing methods are predefined algorithms that do not allow modifications after observing the data. However, in practice, analysts tend to choose a promising algorithm after observing the data; unfortunately, this violates the validity of the conclusion. The i-FWER test allows much flexibility: a human (or a computer program acting on the human’s behalf) may adaptively guide the algorithm in a data-dependent manner. We prove that our test controls FWER if the analysts adhere to a particular protocol of masking and unmasking. We demonstrate via numerical experiments the power of our test under structured non-nulls, and then explore new forms of masking. | Boyan Duan, Aaditya Ramdas, Larry Wasserman | null | null | 2,020 | icml |
Collapsed Amortized Variational Inference for Switching Nonlinear Dynamical Systems | null | We propose an efficient inference method for switching nonlinear dynamical systems. The key idea is to learn an inference network which can be used as a proposal distribution for the continuous latent variables, while performing exact marginalization of the discrete latent variables. This allows us to use the reparameterization trick, and apply end-to-end training with stochastic gradient descent. We show that the proposed method can successfully segment time series data, including videos and 3D human pose, into meaningful “regimes” by using the piece-wise nonlinear dynamics. | Zhe Dong, Bryan Seybold, Kevin Murphy, Hung Bui | null | null | 2,020 | icml |
Equivariant Neural Rendering | null | We propose a framework for learning neural scene representations directly from images, without 3D supervision. Our key insight is that 3D structure can be imposed by ensuring that the learned representation transforms like a real 3D scene. Specifically, we introduce a loss which enforces equivariance of the scene representation with respect to 3D transformations. Our formulation allows us to infer and render scenes in real time while achieving comparable results to models requiring minutes for inference. In addition, we introduce two challenging new datasets for scene representation and neural rendering, including scenes with complex lighting and backgrounds. Through experiments, we show that our model achieves compelling results on these datasets as well as on standard ShapeNet benchmarks. | Emilien Dupont, Miguel Bautista Martin, Alex Colburn, Aditya Sankar, Josh Susskind, Qi Shan | null | null | 2,020 | icml |
The Complexity of Finding Stationary Points with Stochastic Gradient Descent | null | We study the iteration complexity of stochastic gradient descent (SGD) for minimizing the gradient norm of smooth, possibly nonconvex functions. We provide several results, implying that the classical $\mathcal{O}(\epsilon^{-4})$ upper bound (for making the average gradient norm less than $\epsilon$) cannot be improved upon, unless a combination of additional assumptions is made. Notably, this holds even if we limit ourselves to convex quadratic functions. We also show that for nonconvex functions, the feasibility of minimizing gradients with SGD is surprisingly sensitive to the choice of optimality criteria. | Yoel Drori, Ohad Shamir | null | null | 2,020 | icml |
Optimal Non-parametric Learning in Repeated Contextual Auctions with Strategic Buyer | null | We study learning algorithms that optimize revenue in repeated contextual posted-price auctions where a seller interacts with a single strategic buyer that seeks to maximize his cumulative discounted surplus. The buyer’s valuation of a good is a fixed private function of a $d$-dimensional context (feature) vector that describes the good being sold. In contrast to existing studies on repeated contextual auctions with strategic buyer, in our work, the seller is not assumed to know the parametric model that underlies this valuation function. We introduce a novel non-parametric learning algorithm that is horizon-independent and has tight strategic regret upper bound of $\Theta(T^{d/(d+1)})$. We also non-trivially generalize several value-localization techniques of non-contextual repeated auctions to make them effective in the considered contextual non-parametric learning of the buyer valuation function. | Alexey Drutsa | null | null | 2,020 | icml |
Optimization Theory for ReLU Neural Networks Trained with Normalization Layers | null | The current paradigm of deep neural networks has been successful in part due to the use of normalization layers. Normalization layers like Batch Normalization, Layer Normalization and Weight Normalization are ubiquitous in practice as they improve the generalization performance and training speed of neural networks significantly. Nonetheless, the vast majority of current deep learning theory and non-convex optimization literature focuses on the un-normalized setting. We bridge this gap by providing the first global convergence result for 2 layer non-linear neural networks with ReLU activations trained with a normalization layer, namely Weight Normalization. The analysis shows how the introduction of normalization layers changes the optimization landscape and in some settings enables faster convergence as compared with un-normalized neural networks. | Yonatan Dukler, Quanquan Gu, Guido Montufar | null | null | 2,020 | icml |
Is There a Trade-Off Between Fairness and Accuracy? A Perspective Using Mismatched Hypothesis Testing | null | A trade-off between accuracy and fairness is almost taken as a given in the existing literature on fairness in machine learning. Yet, it is not preordained that accuracy should decrease with increased fairness. Novel to this work, we examine fair classification through the lens of mismatched hypothesis testing: trying to find a classifier that distinguishes between two ideal distributions when given two mismatched distributions that are biased. Using Chernoff information, a tool in information theory, we theoretically demonstrate that, contrary to popular belief, there always exist ideal distributions such that optimal fairness and accuracy (with respect to the ideal distributions) are achieved simultaneously: there is no trade-off. Moreover, the same classifier yields the lack of a trade-off with respect to ideal distributions while yielding a trade-off when accuracy is measured with respect to the given (possibly biased) dataset. To complement our main result, we formulate an optimization to find ideal distributions and derive fundamental limits to explain why a trade-off exists on the given biased dataset. We also derive conditions under which active data collection can alleviate the fairness-accuracy trade-off in the real world. Our results lead us to contend that it is problematic to measure accuracy with respect to data that reflects bias, and instead, we should be considering accuracy with respect to ideal, unbiased data. | Sanghamitra Dutta, Dennis Wei, Hazar Yueksel, Pin-Yu Chen, Sijia Liu, Kush Varshney | null | null | 2,020 | icml |
Training Linear Neural Networks: Non-Local Convergence and Complexity Results | null | Linear networks provide valuable insights into the workings of neural networks in general. This paper identifies conditions under which the gradient flow provably trains a linear network, in spite of the non-strict saddle points present in the optimization landscape. This paper also provides the computational complexity of training linear networks with gradient flow. To achieve these results, this work develops a machinery to provably identify the stable set of gradient flow, which then enables us to improve over the state of the art in the literature of linear networks (Bah et al., 2019;Arora et al., 2018a). Crucially, our results appear to be the first to break away from the lazy training regime which has dominated the literature of neural networks. This work requires the network to have a layer with one neuron, which subsumes the networks with a scalar output, but extending the results of this theoretical work to all linear networks remains a challenging open problem. | Armin Eftekhari | null | null | 2,020 | icml |
Estimating Q(s,s’) with Deep Deterministic Dynamics Gradients | null | In this paper, we introduce a novel form of value function, $Q(s, s’)$, that expresses the utility of transitioning from a state $s$ to a neighboring state $s’$ and then acting optimally thereafter. In order to derive an optimal policy, we develop a forward dynamics model that learns to make next-state predictions that maximize this value. This formulation decouples actions from values while still learning off-policy. We highlight the benefits of this approach in terms of value function transfer, learning within redundant action spaces, and learning off-policy from state observations generated by sub-optimal or completely random policies. Code and videos are available at http://sites.google.com/view/qss-paper. | Ashley Edwards, Himanshu Sahni, Rosanne Liu, Jane Hung, Ankit Jain, Rui Wang, Adrien Ecoffet, Thomas Miconi, Charles Isbell, Jason Yosinski | null | null | 2,020 | icml |
Continuous Time Bayesian Networks with Clocks | null | Structured stochastic processes evolving in continuous time present a widely adopted framework to model phenomena occurring in nature and engineering. However, such models are often chosen to satisfy the Markov property to maintain tractability. One of the more popular of such memoryless models are Continuous Time Bayesian Networks (CTBNs). In this work, we lift its restriction to exponential survival times to arbitrary distributions. Current extensions achieve this via auxiliary states, which hinder tractability. To avoid that, we introduce a set of node-wise clocks to construct a collection of graph-coupled semi-Markov chains. We provide algorithms for parameter and structure inference, which make use of local dependencies and conduct experiments on synthetic data and a data-set generated through a benchmark tool for gene regulatory networks. In doing so, we point out advantages compared to current CTBN extensions. | Nicolai Engelmann, Dominik Linzner, Heinz Koeppl | null | null | 2,020 | icml |
Divide and Conquer: Leveraging Intermediate Feature Representations for Quantized Training of Neural Networks | null | The deep layers of modern neural networks extract a rather rich set of features as an input propagates through the network, this paper sets out to harvest these rich intermediate representations for quantization with minimal accuracy loss while significantly reducing the memory footprint and compute intensity of the DNN. This paper utilizes knowledge distillation through teacher-student paradigm (Hinton et al., 2015) in a novel setting that exploits the feature extraction capability of DNNs for higher accuracy quantization. As such, our algorithm logically divides a pretrained full-precision DNN to multiple sections, each of which exposes intermediate features to train a team of students independently in the quantized domain and simply stitching them afterwards. This divide and conquer strategy, makes the training of each student section possible in isolation, speeding up training by enabling parallelization. Experiments on various DNNs (AlexNet, LeNet, MobileNet, ResNet-18, ResNet-20, SVHN and VGG-11) show that, this approach{—}called DCQ (Divide and Conquer Quantization){—}on average, improves the performance of a state-of-the-art quantized training technique, DoReFa-Net (Zhou et al., 2016) by 21.6% and 9.3% for binary and ternary quantization, respectively. Additionally, we show that incorporating DCQ to existing quantized training methods leads to improved accuracies as compared to previously reported by multiple state-of-the-art quantized training methods. | Ahmed Taha Elthakeb, Prannoy Pilligundla, Fatemeh Mireshghallah, Alexander Cloninger, Hadi Esmaeilzadeh | null | null | 2,020 | icml |
Student-Teacher Curriculum Learning via Reinforcement Learning: Predicting Hospital Inpatient Admission Location | null | Accurate and reliable prediction of hospital admission location is important due to resource-constraints and space availability in a clinical setting, particularly when dealing with patients who come from the emergency department. In this work we propose a student-teacher network via reinforcement learning to deal with this specific problem. A representation of the weights of the student network is treated as the state and is fed as an input to the teacher network. The teacher network’s action is to select the most appropriate batch of data to train the student network on from a training set sorted according to entropy. By validating on three datasets, not only do we show that our approach outperforms state-of-the-art methods on tabular data and performs competitively on image recognition, but also that novel curricula are learned by the teacher network. We demonstrate experimentally that the teacher network can actively learn about the student network and guide it to achieve better performance than if trained alone. | Rasheed El-Bouri, David Eyre, Peter Watkinson, Tingting Zhu, David Clifton | null | null | 2,020 | icml |
Distributed Online Optimization over a Heterogeneous Network with Any-Batch Mirror Descent | null | In distributed online optimization over a computing network with heterogeneous nodes, slow nodes can adversely affect the progress of fast nodes, leading to drastic slowdown of the overall convergence process. To address this issue, we consider a new algorithm termed Distributed Any-Batch Mirror Descent (DABMD), which is based on distributed Mirror Descent but uses a fixed per-round computing time to limit the waiting by fast nodes to receive information updates from slow nodes. DABMD is characterized by varying minibatch sizes across nodes. It is applicable to a broader range of problems compared with existing distributed online optimization methods such as those based on dual averaging, and it accommodates time-varying network topology. We study two versions of DABMD, depending on whether the computing nodes average their primal variables via single or multiple consensus iterations. We show that both versions provide strong theoretical performance guarantee, by deriving upperbounds on their expected dynamic regret, which capture the variability in minibatch sizes. Our experimental results show substantial reduction in cost and acceleration in convergence compared with the known best alternative. | Nima Eshraghi, Ben Liang | null | null | 2,020 | icml |
Decision Trees for Decision-Making under the Predict-then-Optimize Framework | null | We consider the use of decision trees for decision-making problems under the predict-then-optimize framework. That is, we would like to first use a decision tree to predict unknown input parameters of an optimization problem, and then make decisions by solving the optimization problem using the predicted parameters. A natural loss function in this framework is to measure the suboptimality of the decisions induced by the predicted input parameters, as opposed to measuring loss using input parameter prediction error. This natural loss function is known in the literature as the Smart Predict-then-Optimize (SPO) loss, and we propose a tractable methodology called SPO Trees (SPOTs) for training decision trees under this loss. SPOTs benefit from the interpretability of decision trees, providing an interpretable segmentation of contextual features into groups with distinct optimal solutions to the optimization problem of interest. We conduct several numerical experiments on synthetic and real data including the prediction of travel times for shortest path problems and predicting click probabilities for news article recommendation. We demonstrate on these datasets that SPOTs simultaneously provide higher quality decisions and significantly lower model complexity than other machine learning approaches (e.g., CART) trained to minimize prediction error. | Adam N. Elmachtoub, Jason Cheuk Nam Liang, Ryan Mcnellis | null | null | 2,020 | icml |
Online mirror descent and dual averaging: keeping pace in the dynamic case | null | Online mirror descent (OMD) and dual averaging (DA)—two fundamental algorithms for online convex optimization—are known to have very similar (and sometimes identical) performance guarantees when used with a fixed learning rate. Under dynamic learning rates, however, OMD is provably inferior to DA and suffers a linear regret, even in common settings such as prediction with expert advice. We modify the OMD algorithm through a simple technique that we call stabilization. We give essentially the same abstract regret bound for OMD with stabilization and for DA by modifying the classical OMD convergence analysis in a careful and modular way that allows for straightforward and flexible proofs. Simple corollaries of these bounds show that OMD with stabilization and DA enjoy the same performance guarantees in many applications—even under dynamic learning rates. We also shed light on the similarities between OMD and DA and show simple conditions under which stabilized-OMD and DA generate the same iterates. | Huang Fang, Nick Harvey, Victor Portella, Michael Friedlander | null | null | 2,020 | icml |
On hyperparameter tuning in general clustering problemsm | null | Tuning hyperparameters for unsupervised learning problems is difficult in general due to the lack of ground truth for validation. However, the success of most clustering methods depends heavily on the correct choice of the involved hyperparameters. Take for example the Lagrange multipliers of penalty terms in semidefinite programming (SDP) relaxations of community detection in networks, or the bandwidth parameter needed in the Gaussian kernel used to construct similarity matrices for spectral clustering. Despite the popularity of these clustering algorithms, there are not many provable methods for tuning these hyperparameters. In this paper, we provide an overarching framework with provable guarantees for tuning hyperparameters in the above class of problems under two different models. Our framework can be augmented with a cross validation procedure to do model selection as well. In a variety of simulation and real data experiments, we show that our framework outperforms other widely used tuning procedures in a broad range of parameter settings. | Xinjie Fan, Yuguang Yue, Purnamrita Sarkar, Y. X. Rachel Wang | null | null | 2,020 | icml |
Latent Bernoulli Autoencoder | null | In this work, we pose the question whether it is possible to design and train an autoencoder model in an end-to-end fashion to learn representations in the multivariate Bernoulli latent space, and achieve performance comparable with the state-of-the-art variational methods. Moreover, we investigate how to generate novel samples and perform smooth interpolation and attributes modification in the binary latent space. To meet our objective, we propose a simplified, deterministic model with a straight-through gradient estimator to learn the binary latents and show its competitiveness with the latest VAE methods. Furthermore, we propose a novel method based on a random hyperplane rounding for sampling and smooth interpolation in the latent space. Our method performs on a par or better than the current state-of-the-art methods on common CelebA, CIFAR-10 and MNIST datasets. | Jiri Fajtl, Vasileios Argyriou, Dorothy Monekosso, Paolo Remagnino | null | null | 2,020 | icml |
Optimal Sequential Maximization: One Interview is Enough! | null | Maximum selection under probabilistic queries \emph{(probabilistic maximization)} is a fundamental algorithmic problem arising in numerous theoretical and practical contexts. We derive the first query-optimal sequential algorithm for probabilistic-maximization. Departing from previous assumptions, the algorithm and performance guarantees apply even for infinitely many items, hence in particular do not require a-priori knowledge of the number of items. The algorithm has linear query complexity, and is optimal also in the streaming setting. To derive these results we consider a probabilistic setting where several candidates for a position are asked multiple questions with the goal of finding who has the highest probability of answering interview questions correctly. Previous work minimized the total number of questions asked by alternating back and forth between the best performing candidates, in a sense, inviting them to multiple interviews. We show that the same order-wise selection accuracy can be achieved by querying the candidates sequentially, never returning to a previously queried candidate. Hence one interview is enough! | Moein Falahatgar, Alon Orlitsky, Venkatadheeraj Pichapati | null | null | 2,020 | icml |
Do GANs always have Nash equilibria? | null | Generative adversarial networks (GANs) represent a zero-sum game between two machine players, a generator and a discriminator, designed to learn the distribution of data. While GANs have achieved state-of-the-art performance in several benchmark learning tasks, GAN minimax optimization still poses great theoretical and empirical challenges. GANs trained using first-order optimization methods commonly fail to converge to a stable solution where the players cannot improve their objective, i.e., the Nash equilibrium of the underlying game. Such issues raise the question of the existence of Nash equilibria in GAN zero-sum games. In this work, we show through theoretical and numerical results that indeed GAN zero-sum games may have no Nash equilibria. To characterize an equilibrium notion applicable to GANs, we consider the equilibrium of a new zero-sum game with an objective function given by a proximal operator applied to the original objective, a solution we call the proximal equilibrium. Unlike the Nash equilibrium, the proximal equilibrium captures the sequential nature of GANs, in which the generator moves first followed by the discriminator. We prove that the optimal generative model in Wasserstein GAN problems provides a proximal equilibrium. Inspired by these results, we propose a new approach, which we call proximal training, for solving GAN problems. We perform several numerical experiments indicating the existence of proximal equilibria in GANs. | Farzan Farnia, Asuman Ozdaglar | null | null | 2,020 | icml |
Spectral Graph Matching and Regularized Quadratic Relaxations: Algorithm and Theory | null | Graph matching, also known as network alignment, aims at recovering the latent vertex correspondence between two unlabeled, edge-correlated weighted graphs. To tackle this task, we propose a spectral method, GRAph Matching by Pairwise eigen-Alignments (GRAMPA), which first constructs a similarity matrix as a weighted sum of outer products between all pairs of eigenvectors of the two graphs, and then outputs a matching by a simple rounding procedure. For a universality class of correlated Wigner models, GRAMPA achieves exact recovery of the latent matching between two graphs with edge correlation $1 - 1/\mathrm{polylog}(n)$ and average degree at least $\mathrm{polylog}(n)$. This matches the state-of-the-art guarantees for polynomial-time algorithms established for correlated Erdős-Rényi graphs, and significantly improves over existing spectral methods. The superiority of GRAMPA is also demonstrated on a variety of synthetic and real datasets, in terms of both statistical accuracy and computational efficiency. | Zhou Fan, Cheng Mao, Yihong Wu, Jiaming Xu | null | null | 2,020 | icml |
Global Concavity and Optimization in a Class of Dynamic Discrete Choice Models | null | Discrete choice models with unobserved heterogeneity are commonly used Econometric models for dynamic Economic behavior which have been adopted in practice to predict behavior of individuals and firms from schooling and job choices to strategic decisions in market competition. These models feature optimizing agents who choose among a finite set of options in a sequence of periods and receive choice-specific payoffs that depend on both variables that are observed by the agent and recorded in the data and variables that are only observed by the agent but not recorded in the data. Existing work in Econometrics assumes that optimizing agents are fully rational and requires finding a functional fixed point to find the optimal policy. We show that in an important class of discrete choice models the value function is globally concave in the policy. That means that simple algorithms that do not require fixed point computation, such as the policy gradient algorithm, globally converge to the optimal policy. This finding can both be used to relax behavioral assumption regarding the optimizing agents and to facilitate Econometric analysis of dynamic behavior. In particular, we demonstrate significant computational advantages in using a simple implementation policy gradient algorithm over existing “nested fixed point” algorithms used in Econometrics. | Yiding Feng, Ekaterina Khmelnitskaya, Denis Nekipelov | null | null | 2,020 | icml |
Why Are Learned Indexes So Effective? | null | A recent trend in algorithm design consists of augmenting classic data structures with machine learning models, which are better suited to reveal and exploit patterns and trends in the input data so to achieve outstanding practical improvements in space occupancy and time efficiency. This is especially known in the context of indexing data structures where, despite few attempts in evaluating their asymptotic efficiency, theoretical results are yet missing in showing that learned indexes are provably better than classic indexes, such as B+ trees and their variants. In this paper, we present the first mathematically-grounded answer to this open problem. We obtain this result by discovering and exploiting a link between the original problem and a mean exit time problem over a proper stochastic process which, we show, is related to the space and time occupancy of those learned indexes. Our general result is then specialised to five well-known distributions: Uniform, Lognormal, Pareto, Exponential, and Gamma; and it is corroborated in precision and robustness by a large set of experiments. | Paolo Ferragina, Fabrizio Lillo, Giorgio Vinciguerra | null | null | 2,020 | icml |
Kernelized Stein Discrepancy Tests of Goodness-of-fit for Time-to-Event Data | null | Survival Analysis and Reliability Theory are concerned with the analysis of time-to-event data, in which observations correspond to waiting times until an event of interest such as death from a particular disease or failure of a component in a mechanical system. This type of data is unique due to the presence of censoring, a type of missing data that occurs when we do not observe the actual time of the event of interest but, instead, we have access to an approximation for it given by random interval in which the observation is known to belong. Most traditional methods are not designed to deal with censoring, and thus we need to adapt them to censored time-to-event data. In this paper, we focus on non-parametric goodness-of-fit testing procedures based on combining the Stein’s method and kernelized discrepancies. While for uncensored data, there is a natural way of implementing a kernelized Stein discrepancy test, for censored data there are several options, each of them with different advantages and disadvantages. In this paper, we propose a collection of kernelized Stein discrepancy tests for time-to-event data, and we study each of them theoretically and empirically; our experimental results show that our proposed methods perform better than existing tests, including previous tests based on a kernelized maximum mean discrepancy. | Tamara Fernandez, Nicolas Rivera, Wenkai Xu, Arthur Gretton | null | null | 2,020 | icml |
How to Train Your Neural ODE: the World of Jacobian and Kinetic Regularization | null | Training neural ODEs on large datasets has not been tractable due to the necessity of allowing the adaptive numerical ODE solver to refine its step size to very small values. In practice this leads to dynamics equivalent to many hundreds or even thousands of layers. In this paper, we overcome this apparent difficulty by introducing a theoretically-grounded combination of both optimal transport and stability regularizations which encourage neural ODEs to prefer simpler dynamics out of all the dynamics that solve a problem well. Simpler dynamics lead to faster convergence and to fewer discretizations of the solver, considerably decreasing wall-clock time without loss in performance. Our approach allows us to train neural ODE-based generative models to the same performance as the unregularized dynamics, with significant reductions in training time. This brings neural ODEs closer to practical relevance in large-scale applications. | Chris Finlay, Joern-Henrik Jacobsen, Levon Nurbekyan, Adam Oberman | null | null | 2,020 | icml |
Implicit Learning Dynamics in Stackelberg Games: Equilibria Characterization, Convergence Analysis, and Empirical Study | null | Contemporary work on learning in continuous games has commonly overlooked the hierarchical decision-making structure present in machine learning problems formulated as games, instead treating them as simultaneous play games and adopting the Nash equilibrium solution concept. We deviate from this paradigm and provide a comprehensive study of learning in Stackelberg games. This work provides insights into the optimization landscape of zero-sum games by establishing connections between Nash and Stackelberg equilibria along with the limit points of simultaneous gradient descent. We derive novel gradient-based learning dynamics emulating the natural structure of a Stackelberg game using the implicit function theorem and provide convergence analysis for deterministic and stochastic updates for zero-sum and general-sum games. Notably, in zero-sum games using deterministic updates, we show the only critical points the dynamics converge to are Stackelberg equilibria and provide a local convergence rate. Empirically, our learning dynamics mitigate rotational behavior and exhibit benefits for training generative adversarial networks compared to simultaneous gradient descent. | Tanner Fiez, Benjamin Chasnov, Lillian Ratliff | null | null | 2,020 | icml |
Generalizing Convolutional Neural Networks for Equivariance to Lie Groups on Arbitrary Continuous Data | null | The translation equivariance of convolutional layers enables CNNs to generalize well on image problems. While translation equivariance provides a powerful inductive bias for images, we often additionally desire equivariance to other transformations, such as rotations, especially for non-image data. We propose a general method to construct a convolutional layer that is equivariant to transformations from any specified Lie group with a surjective exponential map. Incorporating equivariance to a new group requires implementing only the group exponential and logarithm maps, enabling rapid prototyping. Showcasing the simplicity and generality of our method, we apply the same model architecture to images, ball-and-stick molecular data, and Hamiltonian dynamical systems. For Hamiltonian systems, the equivariance of our models is especially impactful, leading to exact conservation of linear and angular momentum. | Marc Finzi, Samuel Stanton, Pavel Izmailov, Andrew Gordon Wilson | null | null | 2,020 | icml |
Can Autonomous Vehicles Identify, Recover From, and Adapt to Distribution Shifts? | null | Out-of-training-distribution (OOD) scenarios are a common challenge of learning agents at deployment, typically leading to arbitrary deductions and poorly-informed decisions. In principle, detection of and adaptation to OOD scenes can mitigate their adverse effects. In this paper, we highlight the limitations of current approaches to novel driving scenes and propose an epistemic uncertainty-aware planning method, called \emph{robust imitative planning} (RIP). Our method can detect and recover from some distribution shifts, reducing the overconfident and catastrophic extrapolations in OOD scenes. If the model’s uncertainty is too great to suggest a safe course of action, the model can instead query the expert driver for feedback, enabling sample-efficient online adaptation, a variant of our method we term \emph{adaptive robust imitative planning} (AdaRIP). Our methods outperform current state-of-the-art approaches in the nuScenes \emph{prediction} challenge, but since no benchmark evaluating OOD detection and adaption currently exists to assess \emph{control}, we introduce an autonomous car novel-scene benchmark, \texttt{CARNOVEL}, to evaluate the robustness of driving agents to a suite of tasks with distribution shifts, where our methods outperform all the baselines. | Angelos Filos, Panagiotis Tigkas, Rowan Mcallister, Nicholas Rhinehart, Sergey Levine, Yarin Gal | null | null | 2,020 | icml |
Information Particle Filter Tree: An Online Algorithm for POMDPs with Belief-Based Rewards on Continuous Domains | null | Planning in Partially Observable Markov Decision Processes (POMDPs) inherently gathers the information necessary to act optimally under uncertainties. The framework can be extended to model pure information gathering tasks by considering belief-based rewards. This allows us to use reward shaping to guide POMDP planning to informative beliefs by using a weighted combination of the original reward and the expected information gain as the objective. In this work we propose a novel online algorithm, Information Particle Filter Tree (IPFT), to solve problems with belief-dependent rewards on continuous domains. It simulates particle-based belief trajectories in a Monte Carlo Tree Search (MCTS) approach to construct a search tree in the belief space. The evaluation shows that the consideration of information gain greatly improves the performance in problems where information gathering is an essential part of the optimal policy. | Johannes Fischer, Ömer Sahin Tas | null | null | 2,020 | icml |
Approximation Guarantees of Local Search Algorithms via Localizability of Set Functions | null | This paper proposes a new framework for providing approximation guarantees of local search algorithms. Local search is a basic algorithm design technique and is widely used for various combinatorial optimization problems. To analyze local search algorithms for set function maximization, we propose a new notion called \emph{localizability} of set functions, which measures how effective local improvement is. Moreover, we provide approximation guarantees of standard local search algorithms under various combinatorial constraints in terms of localizability. The main application of our framework is sparse optimization, for which we show that restricted strong concavity and restricted smoothness of the objective function imply localizability, and further develop accelerated versions of local search algorithms. We conduct experiments in sparse regression and structure learning of graphical models to confirm the practical efficiency of the proposed local search algorithms. | Kaito Fujii | null | null | 2,020 | icml |
p-Norm Flow Diffusion for Local Graph Clustering | null | Local graph clustering and the closely related seed set expansion problem are primitives on graphs that are central to a wide range of analytic and learning tasks such as local clustering, community detection, semi-supervised learning, nodes ranking and feature inference. Prior work on local graph clustering mostly falls into two categories with numerical and combinatorial roots respectively, in this work we draw inspiration from both fields and propose a family of convex optimization formulations based on the idea of diffusion with $p$-norm network flow for $p\in (1,\infty)$. In the context of local clustering, we characterize the optimal solutions for these optimization problems and show their usefulness in finding low conductance cuts around input seed set. In particular, we achieve quadratic approximation of conductance in the case of $p=2$ similar to the Cheeger-type bounds of spectral methods, constant factor approximation when $p\rightarrow\infty$ similar to max-flow based methods, and a smooth transition for general $p$ values in between. Thus, our optimization formulation can be viewed as bridging the numerical and combinatorial approaches, and we can achieve the best of both worlds in terms of speed and noise robustness. We show that the proposed problem can be solved in strongly local running time for $p\ge 2$ and conduct empirical evaluations on both synthetic and real-world graphs to illustrate our approach compares favorably with existing methods. | Kimon Fountoulakis, Di Wang, Shenghao Yang | null | null | 2,020 | icml |
Accelerating the diffusion-based ensemble sampling by non-reversible dynamics | null | Posterior distribution approximation is a central task in Bayesian inference. Stochastic gradient Langevin dynamics (SGLD) and its extensions have been practically used and theoretically studied. While SGLD updates a single particle at a time, ensemble methods that update multiple particles simultaneously have been recently gathering attention. Compared with the naive parallel-chain SGLD that updates multiple particles independently, ensemble methods update particles with their interactions. Thus, these methods are expected to be more particle-efficient than the naive parallel-chain SGLD because particles can be aware of other particles’ behavior through their interactions. Although ensemble methods numerically demonstrated their superior performance, no theoretical guarantee exists to assure such particle-efficiency and it is unclear whether those ensemble methods are really superior to the naive parallel-chain SGLD in the non-asymptotic settings. To cope with this problem, we propose a novel ensemble method that uses a non-reversible Markov chain for the interaction, and we present a non-asymptotic theoretical analysis for our method. Our analysis shows that, for the first time, the interaction causes a faster convergence rate than the naive parallel-chain SGLD in the non-asymptotic setting if the discretization error is appropriately controlled. Numerical experiments show that we can control the discretization error by tuning the interaction appropriately. | Futoshi Futami, Issei Sato, Masashi Sugiyama | null | null | 2,020 | icml |
Beyond UCB: Optimal and Efficient Contextual Bandits with Regression Oracles | null | A fundamental challenge in contextual bandits is to develop flexible, general-purpose algorithms with computational requirements no worse than classical supervised learning tasks such as classification and regression. Algorithms based on regression have shown promising empirical success, but theoretical guarantees have remained elusive except in special cases. We provide the first universal and optimal reduction from contextual bandits to online regression. We show how to transform any oracle for online regression with a given value function class into an algorithm for contextual bandits with the induced policy class, with no overhead in runtime or memory requirements. We characterize the minimax rates for contextual bandits with general, potentially nonparametric function classes, and show that our algorithm is minimax optimal whenever the oracle obtains the optimal rate for regression. Compared to previous results, our algorithm requires no distributional assumptions beyond realizability, and works even when contexts are chosen adversarially. | Dylan Foster, Alexander Rakhlin | null | null | 2,020 | icml |
DessiLBI: Exploring Structural Sparsity of Deep Networks via Differential Inclusion Paths | null | Over-parameterization is ubiquitous nowadays in training neural networks to benefit both optimization in seeking global optima and generalization in reducing prediction error. However, compressive networks are desired in many real world applications and direct training of small networks may be trapped in local optima. In this paper, instead of pruning or distilling over-parameterized models to compressive ones, we propose a new approach based on differential inclusions of inverse scale spaces. Specifically, it generates a family of models from simple to complex ones that couples a pair of parameters to simultaneously train over-parameterized deep models and structural sparsity on weights of fully connected and convolutional layers. Such a differential inclusion scheme has a simple discretization, proposed as Deep structurally splitting Linearized Bregman Iteration (DessiLBI), whose global convergence analysis in deep learning is established that from any initializations, algorithmic iterations converge to a critical point of empirical risks. Experimental evidence shows that DessiLBI achieve comparable and even better performance than the competitive optimizers in exploring the structural sparsity of several widely used backbones on the benchmark datasets. Remarkably, with early stopping, DessiLBI unveils “winning tickets” in early epochs: the effective sparse structure with comparable test accuracy to fully trained over-parameterized models. | Yanwei Fu, Chen Liu, Donghao Li, Xinwei Sun, Jinshan Zeng, Yuan Yao | null | null | 2,020 | icml |
Don’t Waste Your Bits! Squeeze Activations and Gradients for Deep Neural Networks via TinyScript | null | Recent years have witnessed intensive research interests on training deep neural networks (DNNs) more efficiently by quantization-based compression methods, which facilitate DNNs training in two ways: (1) activations are quantized to shrink the memory consumption, and (2) gradients are quantized to decrease the communication cost. However, existing methods mostly use a uniform mechanism that quantizes the values evenly. Such a scheme may cause a large quantization variance and slow down the convergence in practice. In this work, we introduce TinyScript, which applies a non-uniform quantization algorithm to both activations and gradients. TinyScript models the original values by a family of Weibull distributions and searches for ”quantization knobs” that minimize quantization variance. We also discuss the convergence of the non-uniform quantization algorithm on DNNs with varying depths, shedding light on the number of bits required for convergence. Experiments show that TinyScript always obtains lower quantization variance, and achieves comparable model qualities against full precision training using 1-2 bits less than the uniform-based counterpart. | Fangcheng Fu, Yuzheng Hu, Yihan He, Jiawei Jiang, Yingxia Shao, Ce Zhang, Bin Cui | null | null | 2,020 | icml |
Can Stochastic Zeroth-Order Frank-Wolfe Method Converge Faster for Non-Convex Problems? | null | Frank-Wolfe algorithm is an efficient method for optimizing non-convex constrained problems. However, most of existing methods focus on the first-order case. In real-world applications, the gradient is not always available. To address the problem of lacking gradient in many applications, we propose two new stochastic zeroth-order Frank-Wolfe algorithms and theoretically proved that they have a faster convergence rate than existing methods for non-convex problems. Specifically, the function queries oracle of the proposed faster zeroth-order Frank-Wolfe (FZFW) method is $O(\frac{n^{1/2}d}{\epsilon^2})$ which can match the iteration complexity of the first-order counterpart approximately. As for the proposed faster zeroth-order conditional gradient sliding (FZCGS) method, its function queries oracle is improved to $O(\frac{n^{1/2}d}{\epsilon})$, indicating that its iteration complexity is even better than that of its first-order counterpart NCGS-VR. In other words, the iteration complelxity of the accelerated first-order Frank-Wolfe method NCGS-VR is suboptimal. Then, we proposed a new algorithm to improve its IFO (incremental first-order oracle) to $O(\frac{n^{1/2}}{\epsilon})$. At last, the empirical studies on benchmark datasets validate our theoretical results. | Hongchang Gao, Heng Huang | null | null | 2,020 | icml |
Leveraging Frequency Analysis for Deep Fake Image Recognition | null | Deep neural networks can generate images that are astonishingly realistic, so much so that it is often hard for humans to distinguish them from actual photos. These achievements have been largely made possible by Generative Adversarial Networks (GANs). While deep fake images have been thoroughly investigated in the image domain{—}a classical approach from the area of image forensics{—}an analysis in the frequency domain has been missing so far. In this paper,we address this shortcoming and our results reveal that in frequency space, GAN-generated images exhibit severe artifacts that can be easily identified. We perform a comprehensive analysis, showing that these artifacts are consistent across different neural network architectures, data sets, and resolutions. In a further investigation, we demonstrate that these artifacts are caused by upsampling operations found in all current GAN architectures, indicating a structural and fundamental problem in the way images are generated via GANs. Based on this analysis, we demonstrate how the frequency representation can be used to identify deep fake images in an automated way, surpassing state-of-the-art methods. | Joel Frank, Thorsten Eisenhofer, Lea Schönherr, Asja Fischer, Dorothea Kolossa, Thorsten Holz | null | null | 2,020 | icml |
Black-Box Methods for Restoring Monotonicity | null | In many practical applications, heuristic or approximation algorithms are used to efficiently solve the task at hand. However their solutions frequently do not satisfy natural monotonicity properties expected to hold in the optimum. In this work we develop algorithms that are able to restore monotonicity in the parameters of interest. Specifically, given oracle access to a possibly non monotone function, we provide an algorithm that restores monotonicity while degrading the expected value of the function by at most $\epsilon$. The number of queries required is at most logarithmic in $1/\epsilon$ and exponential in the number of parameters. We also give a lower bound showing that this exponential dependence is necessary. Finally, we obtain improved query complexity bounds for restoring the weaker property of $k$-marginal monotonicity. Under this property, every $k$-dimensional projection of the function is required to be monotone. The query complexity we obtain only scales exponentially with $k$ and is polynomial in the number of parameters. | Evangelia Gergatsouli, Brendan Lucier, Christos Tzamos | null | null | 2,020 | icml |
Online Multi-Kernel Learning with Graph-Structured Feedback | null | Multi-kernel learning (MKL) exhibits reliable performance in nonlinear function approximation tasks. Instead of using one kernel, it learns the optimal kernel from a pre-selected dictionary of kernels. The selection of the dictionary has crucial impact on both the performance and complexity of MKL. Specifically, inclusion of a large number of irrelevant kernels may impair the accuracy, and increase the complexity of MKL algorithms. To enhance the accuracy, and alleviate the computational burden, the present paper develops a novel scheme which actively chooses relevant kernels. The proposed framework models the pruned kernel combination as feedback collected from a graph, that is refined ’on the fly.’ Leveraging the random feature approximation, we propose an online scalable multi-kernel learning approach with graph feedback, and prove that the proposed algorithm enjoys sublinear regret. Numerical tests on real datasets demonstrate the effectiveness of the novel approach. | Pouya M Ghari, Yanning Shen | null | null | 2,020 | icml |
Task-Oriented Active Perception and Planning in Environments with Partially Known Semantics | null | We consider an agent that is assigned with a temporal logic task in an environment whose semantic representation is only partially known. We represent the semantics of the environment with a set of state properties, called \emph{atomic propositions} over which, the agent holds a probabilistic belief and updates it as new sensory measurements arrive. The goal is to design a joint perception and planning strategy for the agent that realizes the task with high probability. We develop a planning strategy that takes the semantic uncertainties into account and by doing so provides probabilistic guarantees on the task success. Furthermore, as new data arrive, the belief over the atomic propositions evolves and, subsequently, the planning strategy adapts accordingly. We evaluate the proposed method on various finite-horizon tasks in planar navigation settings where the empirical results show that the proposed method provides reliable task performance that also improves as the knowledge about the environment enhances. | Mahsa Ghasemi, Erdem Bulgur, Ufuk Topcu | null | null | 2,020 | icml |
Multilinear Latent Conditioning for Generating Unseen Attribute Combinations | null | Deep generative models rely on their inductive bias to facilitate generalization, especially for problems with high dimensional data, like images. However, empirical studies have shown that variational autoencoders (VAE) and generative adversarial networks (GAN) lack the generalization ability that occurs naturally in human perception. For example, humans can visualize a woman smiling after only seeing a smiling man. On the contrary, the standard conditional VAE (cVAE) is unable to generate unseen attribute combinations. To this end, we extend cVAE by introducing a multilinear latent conditioning framework that captures the multiplicative interactions between the attributes. We implement two variants of our model and demonstrate their efficacy on MNIST, Fashion-MNIST and CelebA. Altogether, we design a novel conditioning framework that can be used with any architecture to synthesize unseen attribute combinations. | Markos Georgopoulos, Grigorios Chrysos, Maja Pantic, Yannis Panagakis | null | null | 2,020 | icml |
Generalisation error in learning with random features and the hidden manifold model | null | We study generalised linear regression and classification for a synthetically generated dataset encompassing different problems of interest, such as learning with random features, neural networks in the lazy training regime, and the hidden manifold model. We consider the high-dimensional regime and using the replica method from statistical physics, we provide a closed-form expression for the asymptotic generalisation performance in these problems, valid in both the under- and over-parametrised regimes and for a broad choice of generalised linear model loss functions. In particular, we show how to obtain analytically the so-called double descent behaviour for logistic regression with a peak at the interpolation threshold, we illustrate the superiority of orthogonal against random Gaussian projections in learning with random features, and discuss the role played by correlations in the data generated by the hidden manifold model. Beyond the interest in these particular problems, the theoretical formalism introduced in this manuscript provides a path to further extensions to more complex tasks. | Federica Gerace, Bruno Loureiro, Florent Krzakala, Marc Mezard, Lenka Zdeborova | null | null | 2,020 | icml |
Characterizing Distribution Equivalence and Structure Learning for Cyclic and Acyclic Directed Graphs | null | The main approach to defining equivalence among acyclic directed causal graphical models is based on the conditional independence relationships in the distributions that the causal models can generate, in terms of the Markov equivalence. However, it is known that when cycles are allowed in the causal structure, conditional independence may not be a suitable notion for equivalence of two structures, as it does not reflect all the information in the distribution that is useful for identification of the underlying structure. In this paper, we present a general, unified notion of equivalence for linear Gaussian causal directed graphical models, whether they are cyclic or acyclic. In our proposed definition of equivalence, two structures are equivalent if they can generate the same set of data distributions. We also propose a weaker notion of equivalence called quasi-equivalence, which we show is the extent of identifiability from observational data. We propose analytic as well as graphical methods for characterizing the equivalence of two structures. Additionally, we propose a score-based method for learning the structure from observational data, which successfully deals with both acyclic and cyclic structures. | Amiremad Ghassami, Alan Yang, Negar Kiyavash, Kun Zhang | null | null | 2,020 | icml |
Private Counting from Anonymous Messages: Near-Optimal Accuracy with Vanishing Communication Overhead | null | Differential privacy (DP) is a formal notion for quantifying the privacy loss of algorithms. Algorithms in the central model of DP achieve high accuracy but make the strongest trust assumptions whereas those in the local DP model make the weakest trust assumptions but incur substantial accuracy loss. The shuffled DP model [Bittau et al 2017, Erlingsson et al 2019, Cheu et al 19] has recently emerged as a feasible middle ground between the central and local models, providing stronger trust assumptions than the former while promising higher accuracies than the latter. In this paper, we obtain practical communication-efficient algorithms in the shuffled DP model for two basic aggregation primitives used in machine learning: 1) binary summation, and 2) histograms over a moderate number of buckets. Our algorithms achieve accuracy that is arbitrarily close to that of central DP algorithms with an expected communication per user essentially matching what is needed without any privacy constraints! We demonstrate the practicality of our algorithms by experimentally evaluating them and comparing their performance to several widely-used protocols such as Randomized Response [Warner 1965] and RAPPOR [Erlingsson et al. 2014]. | Badih Ghazi, Ravi Kumar, Pasin Manurangsi, Rasmus Pagh | null | null | 2,020 | icml |
Predicting deliberative outcomes | null | We extend structured prediction to deliberative outcomes. Specifically, we learn parameterized games that can map any inputs to equilibria as the outcomes. Standard structured prediction models rely heavily on global scoring functions and are therefore unable to model individual player preferences or how they respond to others asymmetrically. Our games take as input, e.g., UN resolution to be voted on, and map such contexts to initial strategies, player utilities, and interactions. Players are then thought to repeatedly update their strategies in response to weighted aggregates of other players’ choices towards maximizing their individual utilities. The output from the game is a sample from the resulting (near) equilibrium mixed strategy profile. We characterize conditions under which players’ strategies converge to an equilibrium in such games and when the game parameters can be provably recovered from observations. Empirically, we demonstrate on two real voting datasets that our games can recover interpretable strategic interactions, and predict strategies for players in new settings. | Vikas Garg, Tommi Jaakkola | null | null | 2,020 | icml |
Fractal Gaussian Networks: A sparse random graph model based on Gaussian Multiplicative Chaos | null | We propose a novel stochastic network model, called Fractal Gaussian Network (FGN), that embodies well-defined and analytically tractable fractal structures. Such fractal structures have been empirically observed in diverse applications. FGNs interpolate continuously between the popular purely random geometric graphs (a.k.a. the Poisson Boolean network), and random graphs with increasingly fractal behavior. In fact, they form a parametric family of sparse random geometric graphs that are parametrised by a fractality parameter $\nu$ which governs the strength of the fractal structure. FGNs are driven by the latent spatial geometry of Gaussian Multiplicative Chaos (GMC), a canonical model of fractality in its own right. We explore the natural question of detecting the presence of fractality and the problem of parameter estimation based on observed network data. Finally, we explore fractality in community structures by unveiling a natural stochastic block model in the setting of FGNs. | Subhroshekhar Ghosh, Krishna Balasubramanian, Xiaochuan Yang | null | null | 2,020 | icml |
Adaptive Sketching for Fast and Convergent Canonical Polyadic Decomposition | null | This work considers the canonical polyadic decomposition (CPD) of tensors using proximally regularized sketched alternating least squares algorithms. First, it establishes a sublinear rate of convergence for proximally regularized sketched CPD algorithms under two natural conditions that are known to be satisfied by many popular forms of sketching. Second, it demonstrates that the iterative nature of CPD algorithms can be exploited algorithmically to choose more performant sketching rates. This is accomplished by introducing CPD-MWU, a proximally-regularized sketched alternating least squares algorithm that adaptively selects the sketching rate at each iteration. On both synthetic and real data we observe that for noisy tensors CPD-MWU produces decompositions of comparable accuracy to the standard CPD decomposition in less time, often half the time; for ill-conditioned tensors, given the same time budget, CPD-MWU produces decompositions with an order-of-magnitude lower relative error. For a representative real-world dataset CPD-MWU produces residual errors on average 20% lower than CPRAND-MIX and 44% lower than SPALS, two recent sketched CPD algorithms. | Alex Gittens, Kareem Aggour, Bülent Yener | null | null | 2,020 | icml |
Unraveling Meta-Learning: Understanding Feature Representations for Few-Shot Tasks | null | Meta-learning algorithms produce feature extractors which achieve state-of-the-art performance on few-shot classification. While the literature is rich with meta-learning methods, little is known about why the resulting feature extractors perform so well. We develop a better understanding of the underlying mechanics of meta-learning and the difference between models trained using meta-learning and models which are trained classically. In doing so, we introduce and verify several hypotheses for why meta-learned models perform better. Furthermore, we develop a regularizer which boosts the performance of standard training routines for few-shot classification. In many cases, our routine outperforms meta-learning while simultaneously running an order of magnitude faster. | Micah Goldblum, Steven Reich, Liam Fowl, Renkun Ni, Valeriia Cherepanova, Tom Goldstein | null | null | 2,020 | icml |
Interpretable Off-Policy Evaluation in Reinforcement Learning by Highlighting Influential Transitions | null | Off-policy evaluation in reinforcement learning offers the chance of using observational data to improve future outcomes in domains such as healthcare and education, but safe deployment in high stakes settings requires ways of assessing its validity. Traditional measures such as confidence intervals may be insufficient due to noise, limited data and confounding. In this paper we develop a method that could serve as a hybrid human-AI system, to enable human experts to analyze the validity of policy evaluation estimates. This is accomplished by highlighting observations in the data whose removal will have a large effect on the OPE estimate, and formulating a set of rules for choosing which ones to present to domain experts for validation. We develop methods to compute exactly the influence functions for fitted Q-evaluation with two different function classes: kernel-based and linear least squares, as well as importance sampling methods. Experiments on medical simulations and real-world intensive care unit data demonstrate that our method can be used to identify limitations in the evaluation process and make evaluation more robust. | Omer Gottesman, Joseph Futoma, Yao Liu, Sonali Parbhoo, Leo Celi, Emma Brunskill, Finale Doshi-Velez | null | null | 2,020 | icml |
A Distributional Framework For Data Valuation | null | Shapley value is a classic notion from game theory, historically used to quantify the contributions of individuals within groups, and more recently applied to assign values to data points when training machine learning models. Despite its foundational role, a key limitation of the data Shapley framework is that it only provides valuations for points within a fixed data set. It does not account for statistical aspects of the data and does not give a way to reason about points outside the data set. To address these limitations, we propose a novel framework – distributional Shapley– where the value of a point is defined in the context of an underlying data distribution. We prove that distributional Shapley has several desirable statistical properties; for example, the values are stable under perturbations to the data points themselves and to the underlying data distribution. We leverage these properties to develop a new algorithm for estimating values from data, which comes with formal guarantees and runs two orders of magnitude faster than state-of-the-art algorithms for computing the (non distributional) data Shapley values. We apply distributional Shapley to diverse data sets and demonstrate its utility in a data market setting. | Amirata Ghorbani, Michael Kim, James Zou | null | null | 2,020 | icml |
Learning to Navigate The Synthetically Accessible Chemical Space Using Reinforcement Learning | null | Over the last decade, there has been significant progress in the field of machine learning for de novo drug design, particularly in generative modeling of novel chemical structures. However, current generative approaches exhibit a significant challenge: they do not ensure that the proposed molecular structures can be feasibly synthesized nor do they provide the synthesis routes of the proposed small molecules, thereby seriously limiting their practical applicability. In this work, we propose a novel reinforcement learning (RL) setup for de novo drug design: Policy Gradient for Forward Synthesis (PGFS), that addresses this challenge by embedding the concept of synthetic accessibility directly into the de novo drug design system. In this setup, the agent learns to navigate through the immense synthetically accessible chemical space by subjecting initial commercially available molecules to valid chemical reactions at every time step of the iterative virtual synthesis process. The proposed environment for drug discovery provides a highly challenging test-bed for RL algorithms owing to the large state space and high-dimensional continuous action space with hierarchical actions. PGFS achieves state-of-the-art performance in generating structures with high QED and clogP. Moreover, we validate PGFS in an in-silico proof-of-concept associated with three HIV targets. Finally, we describe how the end-to-end training conceptualized in this study represents an important paradigm in radically expanding the synthesizable chemical space and automating the drug discovery process. | Sai Krishna Gottipati, Boris Sattarov, Sufeng Niu, Yashaswi Pathak, Haoran Wei, Shengchao Liu, Shengchao Liu, Simon Blackburn, Karam Thomas, Connor Coley, Jian Tang, Sarath Chandar, Yoshua Bengio | null | null | 2,020 | icml |
Superpolynomial Lower Bounds for Learning One-Layer Neural Networks using Gradient Descent | null | We give the first superpolynomial lower bounds for learning one-layer neural networks with respect to the Gaussian distribution for a broad class of algorithms. In the regression setting, we prove that gradient descent run on any classifier with respect to square loss will fail to achieve small test error in polynomial time. Prior work held only for gradient descent run with small batch sizes and sufficiently smooth classifiers. For classification, we give a stronger result, namely that any statistical query (SQ) algorithm will fail to achieve small test error in polynomial time. Our lower bounds hold for commonly used activations such as ReLU and sigmoid. The core of our result relies on a novel construction of a simple family of neural networks that are exactly orthogonal with respect to all spherically symmetric distributions. | Surbhi Goel, Aravind Gollakota, Zhihan Jin, Sushrut Karmalkar, Adam Klivans | null | null | 2,020 | icml |
SimGANs: Simulator-Based Generative Adversarial Networks for ECG Synthesis to Improve Deep ECG Classification | null | Generating training examples for supervised tasks is a long sought after goal in AI. We study the problem of heart signal electrocardiogram (ECG) synthesis for improved heartbeat classification. ECG synthesis is challenging: the generation of training examples for such biological-physiological systems is not straightforward, due to their dynamic nature in which the various parts of the system interact in complex ways. However, an understanding of these dynamics has been developed for years in the form of mathematical process simulators. We study how to incorporate this knowledge into the generative process by leveraging a biological simulator for the task of ECG classification. Specifically, we use a system of ordinary differential equations representing heart dynamics, and incorporate this ODE system into the optimization process of a generative adversarial network to create biologically plausible ECG training examples. We perform empirical evaluation and show that heart simulation knowledge during the generation process improves ECG classification. | Tomer Golany, Kira Radinsky, Daniel Freedman | null | null | 2,020 | icml |
Scalable Gaussian Process Separation for Kernels with a Non-Stationary Phase | null | The application of Gaussian processes (GPs) to large data sets is limited due to heavy memory and computational requirements. A variety of methods has been proposed to enable scalability, one of which is to exploit structure in the kernel matrix. Previous methods, however, cannot easily deal with mixtures of non-stationary processes. This paper investigates an efficient GP framework, that extends structured kernel interpolation methods to GPs with a non-stationary phase. We particularly treat the separation of nonstationary sources, which is a problem that commonly arises e.g. in spatio-temporal biomedical datasets. Our approach employs multiple sets of non-equidistant inducing points to account for the non-stationarity and retrieve Toeplitz and Kronecker structure in the kernel matrix allowing for efficient inference and kernel learning. Our approach is demonstrated on numerical examples and large spatio-temporal biomedical problems. | Jan Graßhoff, Alexandra Jankowski, Philipp Rostalski | null | null | 2,020 | icml |
Learning the Stein Discrepancy for Training and Evaluating Energy-Based Models without Sampling | null | We present a new method for evaluating and training unnormalized density models. Our approach only requires access to the gradient of the unnormalized model’s log-density. We estimate the Stein discrepancy between the data density p(x) and the model density q(x) based on a vector function of the data. We parameterize this function with a neural network and fit its parameters to maximize this discrepancy. This yields a novel goodness-of-fit test which outperforms existing methods on high dimensional data. Furthermore, optimizing q(x) to minimize this discrepancy produces a novel method for training unnormalized models. This training method can fit large unnormalized models faster than existing approaches. The ability to both learn and compare models is a unique feature of the proposed method. | Will Grathwohl, Kuan-Chieh Wang, Joern-Henrik Jacobsen, David Duvenaud, Richard Zemel | null | null | 2,020 | icml |
Breaking the Curse of Space Explosion: Towards Efficient NAS with Curriculum Search | null | Neural architecture search (NAS) has become an important approach to automatically find effective architectures. To cover all possible good architectures, we need to search in an extremely large search space with billions of candidate architectures. More critically, given a large search space, we may face a very challenging issue of space explosion. However, due to the limitation of computational resources, we can only sample a very small proportion of the architectures, which provides insufficient information for the training. As a result, existing methods may often produce sub-optimal architectures. To alleviate this issue, we propose a curriculum search method that starts from a small search space and gradually incorporates the learned knowledge to guide the search in a large space. With the proposed search strategy, our Curriculum Neural Architecture Search (CNAS) method significantly improves the search efficiency and finds better architectures than existing NAS methods. Extensive experiments on CIFAR-10 and ImageNet demonstrate the effectiveness of the proposed method. | Yong Guo, Yaofo Chen, Yin Zheng, Peilin Zhao, Jian Chen, Junzhou Huang, Mingkui Tan | null | null | 2,020 | icml |
LTF: A Label Transformation Framework for Correcting Label Shift | null | Distribution shift is a major obstacle to the deployment of current deep learning models on real-world problems. Let $Y$ be the class label and $X$ the features. We focus on one type of distribution shift, \emph{ label shift}, where the label marginal distribution $P_Y$ changes but the conditional distribution $P_{X|Y}$ does not. Most existing methods estimate the density ratio between the source- and target-domain label distributions by density matching. However, these methods are either computationally infeasible for large-scale data or restricted to shift correction for discrete labels. In this paper, we propose an end-to-end Label Transformation Framework (LTF) for correcting label shift, which implicitly models the shift of $P_Y$ and the conditional distribution $P_{X|Y}$ using neural networks. Thanks to the flexibility of deep networks, our framework can handle continuous, discrete, and even multi-dimensional labels in a unified way and is scalable to large data. Moreover, for high dimensional $X$, such as images, we find that the redundant information in $X$ severely degrades the estimation accuracy. To remedy this issue, we propose to match the distribution implied by our generative model and the target-domain distribution in a low-dimensional feature space that discards information irrelevant to $Y$. Both theoretical and empirical studies demonstrate the superiority of our method over previous approaches. | Jiaxian Guo, Mingming Gong, Tongliang Liu, Kun Zhang, Dacheng Tao | null | null | 2,020 | icml |
PoWER-BERT: Accelerating BERT Inference via Progressive Word-vector Elimination | null | We develop a novel method, called PoWER-BERT, for improving the inference time of the popular BERT model, while maintaining the accuracy. It works by: a) exploiting redundancy pertaining to word-vectors (intermediate transformer block outputs) and eliminating the redundant vectors. b) determining which word-vectors to eliminate by developing a strategy for measuring their significance, based on the self-attention mechanism. c) learning how many word-vectors to eliminate by augmenting the BERT model and the loss function. Experiments on the standard GLUE benchmark shows that PoWER-BERT achieves up to 4.5x reduction in inference time over BERT with < 1% loss in accuracy. We show that PoWER-BERT offers significantly better trade-off between accuracy and inference time compared to prior methods. We demonstrate that our method attains up to 6.8x reduction in inference time with < 1% loss in accuracy when applied over ALBERT, a highly compressed version of BERT. The code for PoWER-BERT is publicly available at https://github.com/IBM/PoWER-BERT. | Saurabh Goyal, Anamitra Roy Choudhury, Saurabh Raje, Venkatesan Chakaravarthy, Yogish Sabharwal, Ashish Verma | null | null | 2,020 | icml |
Near-Tight Margin-Based Generalization Bounds for Support Vector Machines | null | Support Vector Machines (SVMs) are among the most fundamental tools for binary classification. In its simplest formulation, an SVM produces a hyperplane separating two classes of data using the largest possible margin to the data. The focus on maximizing the margin has been well motivated through numerous generalization bounds. In this paper, we revisit and improve the classic generalization bounds in terms of margins. Furthermore, we complement our new generalization bound by a nearly matching lower bound, thus almost settling the generalization performance of SVMs in terms of margins. | Allan Grønlund, Lior Kamma, Kasper Green Larsen | null | null | 2,020 | icml |
Bootstrap Latent-Predictive Representations for Multitask Reinforcement Learning | null | Learning a good representation is an essential component for deep reinforcement learning (RL). Representation learning is especially important in multitask and partially observable settings where building a representation of the unknown environment is crucial to solve the tasks. Here we introduce Predictions of Bootstrapped Latents (PBL), a simple and flexible self-supervised representation learning algorithm for multitask deep RL. PBL builds on multistep predictive representations of future observations, and focuses on capturing structured information about environment dynamics. Specifically, PBL trains its representation by predicting latent embeddings of future observations. These latent embeddings are themselves trained to be predictive of the aforementioned representations. These predictions form a bootstrapping effect, allowing the agent to learn more about the key aspects of the environment dynamics. In addition, by defining prediction tasks completely in latent space, PBL provides the flexibility of using multimodal observations involving pixel images, language instructions, rewards and more. We show in our experiments that PBL delivers across-the-board improved performance over state of the art deep RL agents in the DMLab-30 multitask setting. | Zhaohan Daniel Guo, Bernardo Avila Pires, Bilal Piot, Jean-Bastien Grill, Florent Altché, Remi Munos, Mohammad Gheshlaghi Azar | null | null | 2,020 | icml |
Communication-Efficient Distributed Stochastic AUC Maximization with Deep Neural Networks | null | In this paper, we study distributed algorithms for large-scale AUC maximization with a deep neural network as a predictive model. Although distributed learning techniques have been investigated extensively in deep learning, they are not directly applicable to stochastic AUC maximization with deep neural networks due to its striking differences from standard loss minimization problems (e.g., cross-entropy). Towards addressing this challenge, we propose and analyze a communication-efficient distributed optimization algorithm based on a \emph{non-convex concave} reformulation of the AUC maximization, in which the communication of both the primal variable and the dual variable between each worker and the parameter server only occurs after multiple steps of gradient-based updates in each worker. Compared with the naive parallel version of an existing algorithm that computes stochastic gradients at individual machines and averages them for updating the model parameter, our algorithm requires a much less number of communication rounds and still achieves linear speedup in theory. To the best of our knowledge, this is the \textbf{first} work that solves the \emph{non-convex concave min-max} problem for AUC maximization with deep neural networks in a communication-efficient distributed manner while still maintaining the linear speedup property in theory. Our experiments on several benchmark datasets show the effectiveness of our algorithm and also confirm our theory. | Zhishuai Guo, Mingrui Liu, Zhuoning Yuan, Li Shen, Wei Liu, Tianbao Yang | null | null | 2,020 | icml |
Safe Deep Semi-Supervised Learning for Unseen-Class Unlabeled Data | null | Deep semi-supervised learning (SSL) has been recently shown very effectively. However, its performance is seriously decreased when the class distribution is mismatched, among which a common situation is that unlabeled data contains some classes not seen in the labeled data. Efforts on this issue remain to be limited. This paper proposes a simple and effective safe deep SSL method to alleviate the harm caused by it. In theory, the result learned from the new method is never worse than learning from merely labeled data, and it is theoretically guaranteed that its generalization approaches the optimal in the order $O(\sqrt{d\ln(n)/n})$, even faster than the convergence rate in supervised learning associated with massive parameters. In the experiment of benchmark data, unlike the existing deep SSL methods which are no longer as good as supervised learning in 40% of unseen-class unlabeled data, the new method can still achieve performance gain in more than 60% of unseen-class unlabeled data. Moreover, the proposal is suitable for many deep SSL algorithms and can be easily extended to handle other cases of class distribution mismatch. | Lan-Zhe Guo, Zhen-Yu Zhang, Yuan Jiang, Yu-Feng Li, Zhi-Hua Zhou | null | null | 2,020 | icml |
Retrieval Augmented Language Model Pre-Training | null | Language model pre-training has been shown to capture a surprising amount of world knowledge, crucial for NLP tasks such as question answering. However, this knowledge is stored implicitly in the parameters of a neural network, requiring ever-larger networks to cover more facts. To capture knowledge in a more modular and interpretable way, we augment language model pre-training with a latent knowledge retriever, which allows the model to retrieve and attend over documents from a large corpus such as Wikipedia, used during pre-training, fine-tuning and inference. For the first time, we show how to pre-train such a knowledge retriever in an unsupervised manner, using masked language modeling as the learning signal and backpropagating through a retrieval step that considers millions of documents. We demonstrate the effectiveness of Retrieval-Augmented Language Model pre-training (REALM) by fine-tuning on the challenging task of Open-domain Question Answering (Open-QA). We compare against state-of-the-art models for both explicit and implicit knowledge storage on three popular Open-QA benchmarks, and find that we outperform all previous methods by a significant margin (4-16% absolute accuracy), while also providing qualitative benefits such as interpretability and modularity. | Kelvin Guu, Kenton Lee, Zora Tung, Panupong Pasupat, Mingwei Chang | null | null | 2,020 | icml |
Online Convex Optimization in the Random Order Model | null | Online Convex Optimization (OCO) is a powerful framework for sequential prediction, portraying the natural uncertainty inherent in data-streams as though the data were generated by an almost omniscient adversary. However, this view, which is often too pessimistic for real-world data, comes with a price. The complexity of solving many important online tasks in this adversarial framework becomes much worse than that of their offline and even stochastic counterparts. In this work we consider a natural random-order version of the OCO model, in which the adversary can choose the set of loss functions, but does not get to choose the order in which they are supplied to the learner; Instead, they are observed in uniformly random order. Focusing on two important families of online tasks, one in which the cumulative loss function is strongly convex (though individual loss functions may not even be convex), and the other being online $k$-PCA, we show that under standard well-conditioned-data assumptions, standard online gradient descent (OGD) methods become much more efficient in the random-order model. In particular, for the first group of tasks OGD guarantees poly-logarithmic regret. In the case of online $k$-PCA, OGD guarantees sublinear regret using only a rank-$k$ SVD on each iteration and memory linear in the size of the solution. | Dan Garber, Gal Korcia, Kfir Levy | null | null | 2,020 | icml |
FedBoost: A Communication-Efficient Algorithm for Federated Learning | null | Communication cost is often a bottleneck in federated learning and other client-based distributed learning scenarios. To overcome this, several gradient compression and model compression algorithms have been proposed. In this work, we propose an alternative approach whereby an ensemble of pre-trained base predictors is trained via federated learning. This method allows for training a model which may otherwise surpass the communication bandwidth and storage capacity of the clients to be learned with on-device data through federated learning. Motivated by language modeling, we prove the optimality of ensemble methods for density estimation for standard empirical risk minimization and agnostic risk minimization. We provide communication-efficient ensemble algorithms for federated learning, where per-round communication cost is independent of the size of the ensemble. Furthermore, unlike works on gradient compression, our proposed approach reduces the communication cost of both server-to-client and client-to-server communication. | Jenny Hamer, Mehryar Mohri, Ananda Theertha Suresh | null | null | 2,020 | icml |
Multidimensional Shape Constraints | null | We propose new multi-input shape constraints across four intuitive categories: complements, diminishers, dominance, and unimodality constraints. We show these shape constraints can be checked and even enforced when training machine-learned models for linear models, generalized additive models, and the nonlinear function class of multi-layer lattice models. Real-world experiments illustrate how the different shape constraints can be used to increase explainability and improve regularization, especially for non-IID train-test distribution shift. | Maya Gupta, Erez Louidor, Oleksandr Mangylov, Nobu Morioka, Taman Narayan, Sen Zhao | null | null | 2,020 | icml |
Let’s Agree to Agree: Neural Networks Share Classification Order on Real Datasets | null | We report a series of robust empirical observations, demonstrating that deep Neural Networks learn the examples in both the training and test sets in a similar order. This phenomenon is observed in all the commonly used benchmarks we evaluated, including many image classification benchmarks, and one text classification benchmark. While this phenomenon is strongest for models of the same architecture, it also crosses architectural boundaries – models of different architectures start by learning the same examples, after which the more powerful model may continue to learn additional examples. We further show that this pattern of results reflects the interplay between the way neural networks learn benchmark datasets. Specifically, when fixing the architecture, we describe synthetic datasets for which this pattern is no longer observed. When fixing the dataset, we show that other learning paradigms may learn the data in a different order. We hypothesize that our results reflect how neural networks discover structure in natural datasets. | Guy Hacohen, Leshem Choshen, Daphna Weinshall | null | null | 2,020 | icml |
Training Binary Neural Networks through Learning with Noisy Supervision | null | This paper formalizes the binarization operations over neural networks from a learning perspective. In contrast to classical hand crafted rules (\eg hard thresholding) to binarize full-precision neurons, we propose to learn a mapping from full-precision neurons to the target binary ones. Each individual weight entry will not be binarized independently. Instead, they are taken as a whole to accomplish the binarization, just as they work together in generating convolution features. To help the training of the binarization mapping, the full-precision neurons after taking sign operations is regarded as some auxiliary supervision signal, which is noisy but still has valuable guidance. An unbiased estimator is therefore introduced to mitigate the influence of the supervision noise. Experimental results on benchmark datasets indicate that the proposed binarization technique attains consistent improvements over baselines. | Kai Han, Yunhe Wang, Yixing Xu, Chunjing Xu, Enhua Wu, Chang Xu | null | null | 2,020 | icml |
Streaming Submodular Maximization under a k-Set System Constraint | null | In this paper, we propose a novel framework that converts streaming algorithms for monotone submodular maximization into streaming algorithms for non-monotone submodular maximization. This reduction readily leads to the currently tightest deterministic approximation ratio for submodular maximization subject to a $k$-matchoid constraint. Moreover, we propose the first streaming algorithm for monotone submodular maximization subject to $k$-extendible and $k$-set system constraints. Together with our proposed reduction, we obtain $O(k\log k)$ and $O(k^2\log k)$ approximation ratio for submodular maximization subject to the above constraints, respectively. We extensively evaluate the empirical performance of our algorithm against the existing work in a series of experiments including finding the maximum independent set in randomly generated graphs, maximizing linear functions over social networks, movie recommendation, Yelp location summarization, and Twitter data summarization. | Ran Haba, Ehsan Kazemi, Moran Feldman, Amin Karbasi | null | null | 2,020 | icml |
Variance Reduced Coordinate Descent with Acceleration: New Method With a Surprising Application to Finite-Sum Problems | null | We propose an accelerated version of stochastic variance reduced coordinate descent – ASVRCD. As other variance reduced coordinate descent methods such as SEGA or SVRCD, our method can deal with problems that include a non-separable and non-smooth regularizer, while accessing a random block of partial derivatives in each iteration only. However, ASVRCD incorporates Nesterov’s momentum, which offers favorable iteration complexity guarantees over both SEGA and SVRCD. As a by-product of our theory, we show that a variant of Katyusha (Allen-Zhu, 2017) is a specific case of ASVRCD, recovering the optimal oracle complexity for the finite sum objective. | Filip Hanzely, Dmitry Kovalev, Peter Richtarik | null | null | 2,020 | icml |
CoMic: Complementary Task Learning & Mimicry for Reusable Skills | null | Learning to control complex bodies and reuse learned behaviors is a longstanding challenge in continuous control. We study the problem of learning reusable humanoid skills by imitating motion capture data and joint training with complementary tasks. We show that it is possible to learn reusable skills through reinforcement learning on 50 times more motion capture data than prior work. We systematically compare a variety of different network architectures across different data regimes both in terms of imitation performance as well as transfer to challenging locomotion tasks. Finally we show that it is possible to interleave the motion capture tracking with training on complementary tasks, enriching the resulting skill space, and enabling the reuse of skills not well covered by the motion capture data such as getting up from the ground or catching a ball. | Leonard Hasenclever, Fabio Pardo, Raia Hadsell, Nicolas Heess, Josh Merel | null | null | 2,020 | icml |
DRWR: A Differentiable Renderer without Rendering for Unsupervised 3D Structure Learning from Silhouette Images | null | Differentiable renderers have been used successfully for unsupervised 3D structure learning from 2D images because they can bridge the gap between 3D and 2D. To optimize 3D shape parameters, current renderers rely on pixel-wise losses between rendered images of 3D reconstructions and ground truth images from corresponding viewpoints. Hence they require interpolation of the recovered 3D structure at each pixel, visibility handling, and optionally evaluating a shading model. In contrast, here we propose a Differentiable Renderer Without Rendering (DRWR) that omits these steps. DRWR only relies on a simple but effective loss that evaluates how well the projections of reconstructed 3D point clouds cover the ground truth object silhouette. Specifically, DRWR employs a smooth silhouette loss to pull the projection of each individual 3D point inside the object silhouette, and a structure-aware repulsion loss to push each pair of projections that fall inside the silhouette far away from each other. Although we omit surface interpolation, visibility handling, and shading, our results demonstrate that DRWR achieves state-of-the-art accuracies under widely used benchmarks, outperforming previous methods both qualitatively and quantitatively. In addition, our training times are significantly lower due to the simplicity of DRWR. | Zhizhong Han, Chao Chen, Yu-Shen Liu, Matthias Zwicker | null | null | 2,020 | icml |
Compressive sensing with un-trained neural networks: Gradient descent finds a smooth approximation | null | Un-trained convolutional neural networks have emerged as highly successful tools for image recovery and restoration. They are capable of solving standard inverse problems such as denoising and compressive sensing with excellent results by simply fitting a neural network model to measurements from a single image or signal without the need for any additional training data. For some applications, this critically requires additional regularization in the form of early stopping the optimization. For signal recovery from a few measurements, however, un-trained convolutional networks have an intriguing self-regularizing property: Even though the network can perfectly fit any image, the network recovers a natural image from few measurements when trained with gradient descent until convergence. In this paper, we provide numerical evidence for this property and study it theoretically. We show that—without any further regularization—an un-trained convolutional neural network can approximately reconstruct signals and images that are sufficiently structured, from a near minimal number of random measurements. | Reinhard Heckel, Mahdi Soltanolkotabi | null | null | 2,020 | icml |
Hierarchically Decoupled Imitation For Morphological Transfer | null | Learning long-range behaviors on complex high-dimensional agents is a fundamental problem in robot learning. For such tasks, we argue that transferring learned information from a morphologically simpler agent can massively improve the sample efficiency of a more complex one. To this end, we propose a hierarchical decoupling of policies into two parts: an independently learned low-level policy and a transferable high-level policy. To remedy poor transfer performance due to mismatch in morphologies, we contribute two key ideas. First, we show that incentivizing a complex agent’s low-level to imitate a simpler agent’s low-level significantly improves zero-shot high-level transfer. Second, we show that KL-regularized training of the high level stabilizes learning and prevents mode-collapse. Finally, on a suite of publicly released navigation and manipulation environments, we demonstrate the applicability of hierarchical transfer on long-range tasks across morphologies. Our code and videos can be found at https://sites.google.com/berkeley.edu/morphology-transfer. | Donald Hejna, Lerrel Pinto, Pieter Abbeel | null | null | 2,020 | icml |
Statistically Preconditioned Accelerated Gradient Method for Distributed Optimization | null | We consider the setting of distributed empirical risk minimization where multiple machines compute the gradients in parallel and a centralized server updates the model parameters. In order to reduce the number of communications required to reach a given accuracy, we propose a preconditioned accelerated gradient method where the preconditioning is done by solving a local optimization problem over a subsampled dataset at the server. The convergence rate of the method depends on the square root of the relative condition number between the global and local loss functions. We estimate the relative condition number for linear prediction models by studying uniform concentration of the Hessians over a bounded domain, which allows us to derive improved convergence rates for existing preconditioned gradient methods and our accelerated method. Experiments on real-world datasets illustrate the benefits of acceleration in the ill-conditioned regime. | Hadrien Hendrikx, Lin Xiao, Sebastien Bubeck, Francis Bach, Laurent Massoulie | null | null | 2,020 | icml |
Gradient-free Online Learning in Continuous Games with Delayed Rewards | null | Motivated by applications to online advertising and recommender systems, we consider a game-theoretic model with delayed rewards and asynchronous, payoff-based feedback. In contrast to previous work on delayed multi-armed bandits, we focus on games with continuous action spaces, and we examine the long-run behavior of strategic agents that follow a no-regret learning policy (but are otherwise oblivious to the game being played, the objectives of their opponents, etc.). To account for the lack of a consistent stream of information (for instance, rewards can arrive out of order and with an a priori unbounded delay), we introduce a gradient-free learning policy where payoff information is placed in a priority queue as it arrives. Somewhat surprisingly, we find that under a standard diagonal concavity assumption, the induced sequence of play converges to Nash Equilibrium (NE) with probability 1, even if the delay between choosing an action and receiving the corresponding reward is unbounded. | Amélie Héliou, Panayotis Mertikopoulos, Zhengyuan Zhou | null | null | 2,020 | icml |
Dynamic Knapsack Optimization Towards Efficient Multi-Channel Sequential Advertising | null | In E-commerce, advertising is essential for merchants to reach their target users. The typical objective is to maximize the advertiser’s cumulative revenue over a period of time under a budget constraint. In real applications, an advertisement (ad) usually needs to be exposed to the same user multiple times until the user finally contributes revenue (e.g., places an order). However, existing advertising systems mainly focus on the immediate revenue with single ad exposures, ignoring the contribution of each exposure to the final conversion, thus usually falls into suboptimal solutions. In this paper, we formulate the sequential advertising strategy optimization as a dynamic knapsack problem. We propose a theoretically guaranteed bilevel optimization framework, which significantly reduces the solution space of the original optimization space while ensuring the solution quality. To improve the exploration efficiency of reinforcement learning, we also devise an effective action space reduction approach. Extensive offline and online experiments show the superior performance of our approaches over state-of-the-art baselines in terms of cumulative revenue. | Xiaotian Hao, Zhaoqing Peng, Yi Ma, Guan Wang, Junqi Jin, Jianye Hao, Shan Chen, Rongquan Bai, Mingzhou Xie, Miao Xu, Zhenzhe Zheng, Chuan Yu, Han Li, Jian Xu, Kun Gai | null | null | 2,020 | icml |
Minimax Rate for Learning From Pairwise Comparisons in the BTL Model | null | We consider the problem of learning the qualities w_1, ... , w_n of a collection of items by performing noisy comparisons among them. We assume there is a fixed “comparison graph” and every neighboring pair of items is compared k times. We will study the popular Bradley-Terry-Luce model, where the probability that item i wins a comparison against j equals w_i/(w_i + w_j). We are interested in how the expected error in estimating the vector w = (w_1, ... , w_n) behaves in the regime when the number of comparisons k is large. Our contribution is the determination of the minimax rate up to a constant factor. We show that this rate is achieved by a simple algorithm based on weighted least squares, with weights determined from the empirical outcomes of the comparisons. This algorithm can be implemented in nearly linear time in the total number of comparisons. | Julien Hendrickx, Alex Olshevsky, Venkatesh Saligrama | null | null | 2,020 | icml |
Optimization and Analysis of the pAp@k Metric for Recommender Systems | null | Modern recommendation and notification systems must be robust to data imbalance, limitations on the number of recommendations/notifications, and heterogeneous engagement profiles across users. The pAp@k metric, which combines the partial-AUC and the precision@k metrics, was recently proposed to evaluate such recommendation systems and has been used in real-world deployments. Conceptually, pAp@k measures the probability of correctly ranking a top-ranked positive instance over top-ranked negative instances. Due to the combinatorial aspect surfaced by top-ranked points, little is known about the characteristics and optimization methods of pAp@k. In this paper, we analyze the learning-theoretic properties of pAp@k, particularly its benefits in evaluating modern recommender systems, and propose novel surrogates that are consistent under certain data regularity conditions. We then provide gradient descent based algorithms to optimize the surrogates directly. Our analysis and experimental evaluation suggest that pAp@k indeed exhibits a certain dual behavior with respect to partial-AUC and precision@k. Moreover, the proposed methods outperform all the baselines in various applications. Taken together, our results motivate the use of pAp@k for large-scale recommender systems with heterogeneous user-engagement. | Gaurush Hiranandani, Warut Vijitbenjaronk, Sanmi Koyejo, Prateek Jain | null | null | 2,020 | icml |
A Natural Lottery Ticket Winner: Reinforcement Learning with Ordinary Neural Circuits | null | We propose a neural information processing system obtained by re-purposing the function of a biological neural circuit model to govern simulated and real-world control tasks. Inspired by the structure of the nervous system of the soil-worm, C. elegans, we introduce ordinary neural circuits (ONCs), defined as the model of biological neural circuits reparameterized for the control of alternative tasks. We first demonstrate that ONCs realize networks with higher maximum flow compared to arbitrary wired networks. We then learn instances of ONCs to control a series of robotic tasks, including the autonomous parking of a real-world rover robot. For reconfiguration of the purpose of the neural circuit, we adopt a search-based optimization algorithm. Ordinary neural circuits perform on par and, in some cases, significantly surpass the performance of contemporary deep learning models. ONC networks are compact, 77% sparser than their counterpart neural controllers, and their neural dynamics are fully interpretable at the cell-level. | Ramin Hasani, Mathias Lechner, Alexander Amini, Daniela Rus, Radu Grosu | null | null | 2,020 | icml |
Towards Non-Parametric Drift Detection via Dynamic Adapting Window Independence Drift Detection (DAWIDD) | null | The notion of concept drift refers to the phenomenon that the distribution, which is underlying the observed data, changes over time; as a consequence machine learning models may become inaccurate and need adjustment. Many online learning schemes include drift detection to actively detect and react to observed changes. Yet, reliable drift detection constitutes a challenging problem in particular in the context of high dimensional data, varying drift characteristics, and the absence of a parametric model such as a classification scheme which reflects the drift. In this paper we present a novel concept drift detection method, Dynamic Adapting Window Independence Drift Detection (DAWIDD), which aims for non-parametric drift detection of diverse drift characteristics. For this purpose, we establish a mathematical equivalence of the presence of drift to the dependency of specific random variables in an according drift process. This allows us to rely on independence tests rather than parametric models or the classification loss, resulting in a fairly robust scheme to universally detect different types of drift, as it is also confirmed in experiments. | Fabian Hinder, André Artelt, Barbara Hammer | null | null | 2,020 | icml |
Learning Task-Agnostic Embedding of Multiple Black-Box Experts for Multi-Task Model Fusion | null | Model fusion is an emerging study in collective learning where heterogeneous experts with private data and learning architectures need to combine their black-box knowledge for better performance. Existing literature achieves this via a local knowledge distillation scheme that transfuses the predictive patterns of each pre-trained expert onto a white-box imitator model, which can be incorporated efficiently into a global model. This scheme however does not extend to multi-task scenarios where different experts were trained to solve different tasks and only part of their distilled knowledge is relevant to a new task. To address this multi-task challenge, we develop a new fusion paradigm that represents each expert as a distribution over a spectrum of predictive prototypes, which are isolated from task-specific information encoded within the prototype distribution. The task-agnostic prototypes can then be reintegrated to generate a new model that solves a new task encoded with a different prototype distribution. The fusion and adaptation performance of the proposed framework is demonstrated empirically on several real-world benchmark datasets. | Nghia Hoang, Thanh Lam, Bryan Kian Hsiang Low, Patrick Jaillet | null | null | 2,020 | icml |
Cost-Effective Interactive Attention Learning with Neural Attention Processes | null | We propose a novel interactive learning framework which we refer to as Interactive Attention Learning (IAL), in which the human supervisors interactively manipulate the allocated attentions, to correct the model’s behaviour by updating the attention-generating network. However, such a model is prone to overfitting due to scarcity of human annotations, and requires costly retraining. Moreover, it is almost infeasible for the human annotators to examine attentions on tons of instances and features. We tackle these challenges by proposing a sample-efficient attention mechanism and a cost-effective reranking algorithm for instances and features. First, we propose Neural Attention Processes (NAP), which is an attention generator that can update its behaviour by incorporating new attention-level supervisions without any retraining. Secondly, we propose an algorithm which prioritizes the instances and the features by their negative impacts, such that the model can yield large improvements with minimal human feedback. We validate IAL on various time-series datasets from multiple domains (healthcare, real-estate, and computer vision) on which it significantly outperforms baselines with conventional attention mechanisms, or without cost-effective reranking, with substantially less retraining and human-model interaction cost. | Jay Heo, Junhyeon Park, Hyewon Jeong, Kwang Joon Kim, Juho Lee, Eunho Yang, Sung Ju Hwang | null | null | 2,020 | icml |
Improving generalization by controlling label-noise information in neural network weights | null | In the presence of noisy or incorrect labels, neural networks have the undesirable tendency to memorize information about the noise. Standard regularization techniques such as dropout, weight decay or data augmentation sometimes help, but do not prevent this behavior. If one considers neural network weights as random variables that depend on the data and stochasticity of training, the amount of memorized information can be quantified with the Shannon mutual information between weights and the vector of all training labels given inputs, $I(w; \mathbf{y} \mid \mathbf{x})$. We show that for any training algorithm, low values of this term correspond to reduction in memorization of label-noise and better generalization bounds. To obtain these low values, we propose training algorithms that employ an auxiliary network that predicts gradients in the final layers of a classifier without accessing labels. We illustrate the effectiveness of our approach on versions of MNIST, CIFAR-10, and CIFAR-100 corrupted with various noise models, and on a large-scale dataset Clothing1M that has noisy labels. | Hrayr Harutyunyan, Kyle Reing, Greg Ver Steeg, Aram Galstyan | null | null | 2,020 | icml |
One Policy to Control Them All: Shared Modular Policies for Agent-Agnostic Control | null | Reinforcement learning is typically concerned with learning control policies tailored to a particular agent. We investigate whether there exists a single global policy that can generalize to control a wide variety of agent morphologies – ones in which even dimensionality of state and action spaces changes. We propose to express this global policy as a collection of identical modular neural networks, dubbed as Shared Modular Policies (SMP), that correspond to each of the agent’s actuators. Every module is only responsible for controlling its corresponding actuator and receives information from only its local sensors. In addition, messages are passed between modules, propagating information between distant modules. We show that a single modular policy can successfully generate locomotion behaviors for several planar agents with different skeletal structures such as monopod hoppers, quadrupeds, bipeds, and generalize to variants not seen during training – a process that would normally require training and manual hyperparameter tuning for each morphology. We observe that a wide variety of drastically diverse locomotion styles across morphologies as well as centralized coordination emerges via message passing between decentralized modules purely from the reinforcement learning objective. Videos and code at https://huangwl18.github.io/modular-rl/ | Wenlong Huang, Igor Mordatch, Deepak Pathak | null | null | 2,020 | icml |
Optimizing Dynamic Structures with Bayesian Generative Search | null | Kernel selection for kernel-based methods is prohibitively expensive due to the NP-hard nature of discrete optimization. Since gradient-based optimizers are not applicable due to the lack of a differentiable objective function, many state-of-the-art solutions resort to heuristic search or gradient-free optimization. These approaches, however, require imposing restrictive assumptions on the explorable space of structures such as limiting the active candidate pool, thus depending heavily on the intuition of domain experts. This paper instead proposes \textbf{DTERGENS}, a novel generative search framework that constructs and optimizes a high-performance composite kernel expressions generator. \textbf{DTERGENS} does not restrict the space of candidate kernels and is capable of obtaining flexible length expressions by jointly optimizing a generative termination criterion. We demonstrate that our framework explores more diverse kernels and obtains better performance than state-of-the-art approaches on many real-world predictive tasks. | Minh Hoang, Carleton Kingsford | null | null | 2,020 | icml |
Lifted Disjoint Paths with Application in Multiple Object Tracking | null | We present an extension to the disjoint paths problem in which additional lifted edges are introduced to provide path connectivity priors. We call the resulting optimization problem the lifted disjoint paths problem. We show that this problem is NP-hard by reduction from integer multicommodity flow and 3-SAT. To enable practical global optimization, we propose several classes of linear inequalities that produce a high-quality LP-relaxation. Additionally, we propose efficient cutting plane algorithms for separating the proposed linear inequalities. The lifted disjoint path problem is a natural model for multiple object tracking and allows an elegant mathematical formulation for long range temporal interactions. Lifted edges help to prevent id switches and to re-identify persons. Our lifted disjoint paths tracker achieves nearly optimal assignments with respect to input detections. As a consequence, it leads on all three main benchmarks of the MOT challenge, improving significantly over state-of-the-art. | Andrea Hornakova, Roberto Henschel, Bodo Rosenhahn, Paul Swoboda | null | null | 2,020 | icml |
“Other-Play” for Zero-Shot Coordination | null | We consider the problem of zero-shot coordination - constructing AI agents that can coordinate with novel partners they have not seen before (e.g.humans). Standard Multi-Agent Reinforcement Learning (MARL) methods typically focus on the self-play (SP) setting where agents construct strategies by playing the game with themselves repeatedly. Unfortunately, applying SP naively to the zero-shot coordination problem can produce agents that establish highly specialized conventions that do not carry over to novel partners they have not been trained with. We introduce a novel learning algorithm called other-play (OP), that enhances self-play by looking for more robust strategies. We characterize OP theoretically as well as experimentally. We study the cooperative card game Hanabi and show that OP agents achieve higher scores when paired with independently trained agents as well as with human players than SP agents. | Hengyuan Hu, Adam Lerer, Alex Peysakhovich, Jakob Foerster | null | null | 2,020 | icml |
Parameterized Rate-Distortion Stochastic Encoder | null | We propose a novel gradient-based tractable approach for the Blahut-Arimoto (BA) algorithm to compute the rate-distortion function where the BA algorithm is fully parameterized. This results in a rich and flexible framework to learn a new class of stochastic encoders, termed PArameterized RAte-DIstortion Stochastic Encoder (PARADISE). The framework can be applied to a wide range of settings from semi-supervised, multi-task to supervised and robust learning. We show that the training objective of PARADISE can be seen as a form of regularization that helps improve generalization. With an emphasis on robust learning we further develop a novel posterior matching objective to encourage smoothness on the loss function and show that PARADISE can significantly improve interpretability as well as robustness to adversarial attacks on the CIFAR-10 and ImageNet datasets. In particular, on the CIFAR-10 dataset, our model reduces standard and adversarial error rates in comparison to the state-of-the-art by 50% and 41%, respectively without the expensive computational cost of adversarial training. | Quan Hoang, Trung Le, Dinh Phung | null | null | 2,020 | icml |
Black-Box Variational Inference as a Parametric Approximation to Langevin Dynamics | null | Variational inference (VI) and Markov chain Monte Carlo (MCMC) are approximate posterior inference algorithms that are often said to have complementary strengths, with VI being fast but biased and MCMC being slower but asymptotically unbiased. In this paper, we analyze gradient-based MCMC and VI procedures and find theoretical and empirical evidence that these procedures are not as different as one might think. In particular, a close examination of the Fokker-Planck equation that governs the Langevin dynamics (LD) MCMC procedure reveals that LD implicitly follows a gradient flow that corresponds to a variational inference procedure based on optimizing a nonparametric normalizing flow. This result suggests that the transient bias of LD (due to the Markov chain not having burned in) may track that of VI (due to the optimizer not having converged), up to differences due to VI’s asymptotic bias and parameterization. Empirically, we find that the transient biases of these algorithms (and their momentum-accelerated counterparts) do evolve similarly. This suggests that practitioners with a limited time budget may get more accurate results by running an MCMC procedure (even if it’s far from burned in) than a VI procedure, as long as the variance of the MCMC estimator can be dealt with (e.g., by running many parallel chains). | Matthew Hoffman, Yian Ma | null | null | 2,020 | icml |
Accelerated Stochastic Gradient-free and Projection-free Methods | null | In the paper, we propose a class of accelerated stochastic gradient-free and projection-free (a.k.a., zeroth-order Frank-Wolfe) methods to solve the constrained stochastic and finite-sum nonconvex optimization. Specifically, we propose an accelerated stochastic zeroth-order Frank-Wolfe (Acc-SZOFW) method based on the variance reduced technique of SPIDER/SpiderBoost and a novel momentum accelerated technique. Moreover, under some mild conditions, we prove that the Acc-SZOFW has the function query complexity of $O(d\sqrt{n}\epsilon^{-2})$ for finding an $\epsilon$-stationary point in the finite-sum problem, which improves the exiting best result by a factor of $O(\sqrt{n}\epsilon^{-2})$, and has the function query complexity of $O(d\epsilon^{-3})$ in the stochastic problem, which improves the exiting best result by a factor of $O(\epsilon^{-1})$. To relax the large batches required in the Acc-SZOFW, we further propose a novel accelerated stochastic zeroth-order Frank-Wolfe (Acc-SZOFW*) based on a new variance reduced technique of STORM, which still reaches the function query complexity of $O(d\epsilon^{-3})$ in the stochastic problem without relying on any large batches. In particular, we present an accelerated framework of the Frank-Wolfe methods based on the proposed momentum accelerated technique. The extensive experimental results on black-box adversarial attack and robust black-box classification demonstrate the efficiency of our algorithms. | Feihu Huang, Lue Tao, Songcan Chen | null | null | 2,020 | icml |
Improving Transformer Optimization Through Better Initialization | null | The Transformer architecture has achieved considerable success recently; the key component of the Transformer is the attention layer that enables the model to focus on important regions within an input sequence. Gradient optimization with attention layers can be notoriously difficult requiring tricks such as learning rate warmup to prevent divergence. As Transformer models are becoming larger and more expensive to train, recent research has focused on understanding and improving optimization in these architectures. In this work our contributions are two-fold: we first investigate and empirically validate the source of optimization problems in the encoder-decoder Transformer architecture; we then propose a new weight initialization scheme with theoretical justification, that enables training without warmup or layer normalization. Empirical results on public machine translation benchmarks show that our approach achieves leading accuracy, allowing to train deep Transformer models with 200 layers in both encoder and decoder (over 1000 attention/MLP blocks) without difficulty. Code for this work is available here: \url{https://github.com/layer6ai-labs/T-Fixup}. | Xiao Shi Huang, Felipe Perez, Jimmy Ba, Maksims Volkovs | null | null | 2,020 | icml |
Communication-Efficient Distributed PCA by Riemannian Optimization | null | In this paper, we study the leading eigenvector problem in a statistically distributed setting and propose a communication-efficient algorithm based on Riemannian optimization, which trades local computation for global communication. Theoretical analysis shows that the proposed algorithm linearly converges to the centralized empirical risk minimization solution regarding the number of communication rounds. When the number of data points in local machines is sufficiently large, the proposed algorithm achieves a significant reduction of communication cost over existing distributed PCA algorithms. Superior performance in terms of communication cost of the proposed algorithm is verified on real-world and synthetic datasets. | Long-Kai Huang, Sinno Pan | null | null | 2,020 | icml |
Curvature-corrected learning dynamics in deep neural networks | null | Deep neural networks exhibit complex learning dynamics due to their non-convex loss landscapes. Second-order optimization methods facilitate learning dynamics by compensating for ill-conditioned curvature. In this work, we investigate how curvature correction modifies the learning dynamics in deep linear neural networks and provide analytical solutions. We derive a generalized conservation law that preserves the path of parameter dynamics from curvature correction, which shows that curvature correction only modifies the temporal profiles of dynamics along the path. We show that while curvature correction accelerates the convergence dynamics of the input-output map, it can also negatively affect the generalization performance. Our analysis also reveals an undesirable effect of curvature correction that compromises stability of parameters dynamics during learning, especially with block-diagonal approximation of natural gradient descent. We introduce fractional curvature correction that resolves this problem while retaining most of the acceleration benefits of full curvature correction. | Dongsung Huh | null | null | 2,020 | icml |
Generating Programmatic Referring Expressions via Program Synthesis | null | Incorporating symbolic reasoning into machine learning algorithms is a promising approach to improve performance on learning tasks that require logical reasoning. We study the problem of generating a programmatic variant of referring expressions that we call referring relational programs. In particular, given a symbolic representation of an image and a target object in that image, the goal is to generate a relational program that uniquely identifies the target object in terms of its attributes and its relations to other objects in the image. We propose a neurosymbolic program synthesis algorithm that combines a policy neural network with enumerative search to generate such relational programs. The policy neural network employs a program interpreter that provides immediate feedback on the consequences of the decisions made by the policy, and also takes into account the uncertainty in the symbolic representation of the image. We evaluate our algorithm on challenging benchmarks based on the CLEVR dataset, and demonstrate that our approach significantly outperforms several baselines. | Jiani Huang, Calvin Smith, Osbert Bastani, Rishabh Singh, Aws Albarghouthi, Mayur Naik | null | null | 2,020 | icml |
XTREME: A Massively Multilingual Multi-task Benchmark for Evaluating Cross-lingual Generalisation | null | Much recent progress in applications of machine learning models to NLP has been driven by benchmarks that evaluate models across a wide variety of tasks. However, these broad-coverage benchmarks have been mostly limited to English, and despite an increasing interest in multilingual models, a benchmark that enables the comprehensive evaluation of such methods on a diverse range of languages and tasks is still missing. To this end, we introduce the Cross-lingual TRansfer Evaluation of Multilingual Encoders (XTREME) benchmark, a multi-task benchmark for evaluating the cross-lingual generalization capabilities of multilingual representations across 40 languages and 9 tasks. We demonstrate that while models tested on English reach human performance on many tasks, there is still a sizable gap in the performance of cross-lingually transferred models, particularly on syntactic and sentence retrieval tasks. There is also a wide spread of results across languages. We will release the benchmark to encourage research on cross-lingual learning methods that transfer linguistic knowledge across a diverse and representative set of languages and tasks. | Junjie Hu, Sebastian Ruder, Aditya Siddhant, Graham Neubig, Orhan Firat, Melvin Johnson | null | null | 2,020 | icml |
Deep Graph Random Process for Relational-Thinking-Based Speech Recognition | null | Lying at the core of human intelligence, relational thinking is characterized by initially relying on innumerable unconscious percepts pertaining to relations between new sensory signals and prior knowledge, consequently becoming a recognizable concept or object through coupling and transformation of these percepts. Such mental processes are difficult to model in real-world problems such as in conversational automatic speech recognition (ASR), as the percepts (if they are modelled as graphs indicating relationships among utterances) are supposed to be innumerable and not directly observable. In this paper, we present a Bayesian nonparametric deep learning method called deep graph random process (DGP) that can generate an infinite number of probabilistic graphs representing percepts. We further provide a closed-form solution for coupling and transformation of these percept graphs for acoustic modeling. Our approach is able to successfully infer relations among utterances without using any relational data during training. Experimental evaluations on ASR tasks including CHiME-2 and CHiME-5 demonstrate the effectiveness and benefits of our method. | Hengguan Huang, Fuzhao Xue, Hao Wang, Ye Wang | null | null | 2,020 | icml |
Fast Deterministic CUR Matrix Decomposition with Accuracy Assurance | null | The deterministic CUR matrix decomposition is a low-rank approximation method to analyze a data matrix. It has attracted considerable attention due to its high interpretability, which results from the fact that the decomposed matrices consist of subsets of the original columns and rows of the data matrix. The subset is obtained by optimizing an objective function with sparsity-inducing norms via coordinate descent. However, the existing algorithms for optimization incur high computation costs. This is because coordinate descent iteratively updates all the parameters in the objective until convergence. This paper proposes a fast deterministic CUR matrix decomposition. Our algorithm safely skips unnecessary updates by efficiently evaluating the optimality conditions for the parameters to be zeros. In addition, we preferentially update the parameters that must be nonzeros. Theoretically, our approach guarantees the same result as the original approach. Experiments demonstrate that our algorithm speeds up the deterministic CUR while achieving the same accuracy. | Yasutoshi Ida, Sekitoshi Kanai, Yasuhiro Fujiwara, Tomoharu Iwata, Koh Takeuchi, Hisashi Kashima | null | null | 2,020 | icml |
Inverse Active Sensing: Modeling and Understanding Timely Decision-Making | null | Evidence-based decision-making entails collecting (costly) observations about an underlying phenomenon of interest, and subsequently committing to an (informed) decision on the basis of accumulated evidence. In this setting, *active sensing* is the goal-oriented problem of efficiently selecting which acquisitions to make, and when and what decision to settle on. As its complement, *inverse active sensing* seeks to uncover an agent’s preferences and strategy given their observable decision-making behavior. In this paper, we develop an expressive, unified framework for the general setting of evidence-based decision-making under endogenous, context-dependent time pressure—which requires negotiating (subjective) tradeoffs between accuracy, speediness, and cost of information. Using this language, we demonstrate how it enables *modeling* intuitive notions of surprise, suspense, and optimality in decision strategies (the forward problem). Finally, we illustrate how this formulation enables *understanding* decision-making behavior by quantifying preferences implicit in observed decision strategies (the inverse problem). | Daniel Jarrett, Mihaela Van Der Schaar | null | null | 2,020 | icml |
Extra-gradient with player sampling for faster convergence in n-player games | null | Data-driven modeling increasingly requires to find a Nash equilibrium in multi-player games, e.g. when training GANs. In this paper, we analyse a new extra-gradient method for Nash equilibrium finding, that performs gradient extrapolations and updates on a random subset of players at each iteration. This approach provably exhibits a better rate of convergence than full extra-gradient for non-smooth convex games with noisy gradient oracle. We propose an additional variance reduction mechanism to obtain speed-ups in smooth convex games. Our approach makes extrapolation amenable to massive multiplayer settings, and brings empirical speed-ups, in particular when using a heuristic cyclic sampling scheme. Most importantly, it allows to train faster and better GANs and mixtures of GANs. | Samy Jelassi, Carles Domingo-Enrich, Damien Scieur, Arthur Mensch, Joan Bruna | null | null | 2,020 | icml |
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