Models, code, and papers for "Will Dabney":

Distributional Reinforcement Learning with Quantile Regression

Oct 27, 2017
Will Dabney, Mark Rowland, Marc G. Bellemare, Rémi Munos

In reinforcement learning an agent interacts with the environment by taking actions and observing the next state and reward. When sampled probabilistically, these state transitions, rewards, and actions can all induce randomness in the observed long-term return. Traditionally, reinforcement learning algorithms average over this randomness to estimate the value function. In this paper, we build on recent work advocating a distributional approach to reinforcement learning in which the distribution over returns is modeled explicitly instead of only estimating the mean. That is, we examine methods of learning the value distribution instead of the value function. We give results that close a number of gaps between the theoretical and algorithmic results given by Bellemare, Dabney, and Munos (2017). First, we extend existing results to the approximate distribution setting. Second, we present a novel distributional reinforcement learning algorithm consistent with our theoretical formulation. Finally, we evaluate this new algorithm on the Atari 2600 games, observing that it significantly outperforms many of the recent improvements on DQN, including the related distributional algorithm C51.


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Autoregressive Quantile Networks for Generative Modeling

Jun 14, 2018
Georg Ostrovski, Will Dabney, Rémi Munos

We introduce autoregressive implicit quantile networks (AIQN), a fundamentally different approach to generative modeling than those commonly used, that implicitly captures the distribution using quantile regression. AIQN is able to achieve superior perceptual quality and improvements in evaluation metrics, without incurring a loss of sample diversity. The method can be applied to many existing models and architectures. In this work we extend the PixelCNN model with AIQN and demonstrate results on CIFAR-10 and ImageNet using Inception score, FID, non-cherry-picked samples, and inpainting results. We consistently observe that AIQN yields a highly stable algorithm that improves perceptual quality while maintaining a highly diverse distribution.

* ICML 2018 

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A Distributional Perspective on Reinforcement Learning

Jul 21, 2017
Marc G. Bellemare, Will Dabney, Rémi Munos

In this paper we argue for the fundamental importance of the value distribution: the distribution of the random return received by a reinforcement learning agent. This is in contrast to the common approach to reinforcement learning which models the expectation of this return, or value. Although there is an established body of literature studying the value distribution, thus far it has always been used for a specific purpose such as implementing risk-aware behaviour. We begin with theoretical results in both the policy evaluation and control settings, exposing a significant distributional instability in the latter. We then use the distributional perspective to design a new algorithm which applies Bellman's equation to the learning of approximate value distributions. We evaluate our algorithm using the suite of games from the Arcade Learning Environment. We obtain both state-of-the-art results and anecdotal evidence demonstrating the importance of the value distribution in approximate reinforcement learning. Finally, we combine theoretical and empirical evidence to highlight the ways in which the value distribution impacts learning in the approximate setting.

* ICML 2017 

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Implicit Quantile Networks for Distributional Reinforcement Learning

Jun 14, 2018
Will Dabney, Georg Ostrovski, David Silver, Rémi Munos

In this work, we build on recent advances in distributional reinforcement learning to give a generally applicable, flexible, and state-of-the-art distributional variant of DQN. We achieve this by using quantile regression to approximate the full quantile function for the state-action return distribution. By reparameterizing a distribution over the sample space, this yields an implicitly defined return distribution and gives rise to a large class of risk-sensitive policies. We demonstrate improved performance on the 57 Atari 2600 games in the ALE, and use our algorithm's implicitly defined distributions to study the effects of risk-sensitive policies in Atari games.

* ICML 2018 

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The Termination Critic

Feb 26, 2019
Anna Harutyunyan, Will Dabney, Diana Borsa, Nicolas Heess, Remi Munos, Doina Precup

In this work, we consider the problem of autonomously discovering behavioral abstractions, or options, for reinforcement learning agents. We propose an algorithm that focuses on the termination condition, as opposed to -- as is common -- the policy. The termination condition is usually trained to optimize a control objective: an option ought to terminate if another has better value. We offer a different, information-theoretic perspective, and propose that terminations should focus instead on the compressibility of the option's encoding -- arguably a key reason for using abstractions. To achieve this algorithmically, we leverage the classical options framework, and learn the option transition model as a "critic" for the termination condition. Using this model, we derive gradients that optimize the desired criteria. We show that the resulting options are non-trivial, intuitively meaningful, and useful for learning and planning.

* AISTATS 2019 

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An Analysis of Categorical Distributional Reinforcement Learning

Feb 22, 2018
Mark Rowland, Marc G. Bellemare, Will Dabney, Rémi Munos, Yee Whye Teh

Distributional approaches to value-based reinforcement learning model the entire distribution of returns, rather than just their expected values, and have recently been shown to yield state-of-the-art empirical performance. This was demonstrated by the recently proposed C51 algorithm, based on categorical distributional reinforcement learning (CDRL) [Bellemare et al., 2017]. However, the theoretical properties of CDRL algorithms are not yet well understood. In this paper, we introduce a framework to analyse CDRL algorithms, establish the importance of the projected distributional Bellman operator in distributional RL, draw fundamental connections between CDRL and the Cram\'er distance, and give a proof of convergence for sample-based categorical distributional reinforcement learning algorithms.


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Statistics and Samples in Distributional Reinforcement Learning

Feb 21, 2019
Mark Rowland, Robert Dadashi, Saurabh Kumar, Rémi Munos, Marc G. Bellemare, Will Dabney

We present a unifying framework for designing and analysing distributional reinforcement learning (DRL) algorithms in terms of recursively estimating statistics of the return distribution. Our key insight is that DRL algorithms can be decomposed as the combination of some statistical estimator and a method for imputing a return distribution consistent with that set of statistics. With this new understanding, we are able to provide improved analyses of existing DRL algorithms as well as construct a new algorithm (EDRL) based upon estimation of the expectiles of the return distribution. We compare EDRL with existing methods on a variety of MDPs to illustrate concrete aspects of our analysis, and develop a deep RL variant of the algorithm, ER-DQN, which we evaluate on the Atari-57 suite of games.


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Low-pass Recurrent Neural Networks - A memory architecture for longer-term correlation discovery

May 13, 2018
Thomas Stepleton, Razvan Pascanu, Will Dabney, Siddhant M. Jayakumar, Hubert Soyer, Remi Munos

Reinforcement learning (RL) agents performing complex tasks must be able to remember observations and actions across sizable time intervals. This is especially true during the initial learning stages, when exploratory behaviour can increase the delay between specific actions and their effects. Many new or popular approaches for learning these distant correlations employ backpropagation through time (BPTT), but this technique requires storing observation traces long enough to span the interval between cause and effect. Besides memory demands, learning dynamics like vanishing gradients and slow convergence due to infrequent weight updates can reduce BPTT's practicality; meanwhile, although online recurrent network learning is a developing topic, most approaches are not efficient enough to use as replacements. We propose a simple, effective memory strategy that can extend the window over which BPTT can learn without requiring longer traces. We explore this approach empirically on a few tasks and discuss its implications.


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Fast Task Inference with Variational Intrinsic Successor Features

Jun 12, 2019
Steven Hansen, Will Dabney, Andre Barreto, Tom Van de Wiele, David Warde-Farley, Volodymyr Mnih

It has been established that diverse behaviors spanning the controllable subspace of an Markov decision process can be trained by rewarding a policy for being distinguishable from other policies \citep{gregor2016variational, eysenbach2018diversity, warde2018unsupervised}. However, one limitation of this formulation is generalizing behaviors beyond the finite set being explicitly learned, as is needed for use on subsequent tasks. Successor features \citep{dayan93improving, barreto2017successor} provide an appealing solution to this generalization problem, but require defining the reward function as linear in some grounded feature space. In this paper, we show that these two techniques can be combined, and that each method solves the other's primary limitation. To do so we introduce Variational Intrinsic Successor FeatuRes (VISR), a novel algorithm which learns controllable features that can be leveraged to provide enhanced generalization and fast task inference through the successor feature framework. We empirically validate VISR on the full Atari suite, in a novel setup wherein the rewards are only exposed briefly after a long unsupervised phase. Achieving human-level performance on 14 games and beating all baselines, we believe VISR represents a step towards agents that rapidly learn from limited feedback.


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The Cramer Distance as a Solution to Biased Wasserstein Gradients

May 30, 2017
Marc G. Bellemare, Ivo Danihelka, Will Dabney, Shakir Mohamed, Balaji Lakshminarayanan, Stephan Hoyer, Rémi Munos

The Wasserstein probability metric has received much attention from the machine learning community. Unlike the Kullback-Leibler divergence, which strictly measures change in probability, the Wasserstein metric reflects the underlying geometry between outcomes. The value of being sensitive to this geometry has been demonstrated, among others, in ordinal regression and generative modelling. In this paper we describe three natural properties of probability divergences that reflect requirements from machine learning: sum invariance, scale sensitivity, and unbiased sample gradients. The Wasserstein metric possesses the first two properties but, unlike the Kullback-Leibler divergence, does not possess the third. We provide empirical evidence suggesting that this is a serious issue in practice. Leveraging insights from probabilistic forecasting we propose an alternative to the Wasserstein metric, the Cram\'er distance. We show that the Cram\'er distance possesses all three desired properties, combining the best of the Wasserstein and Kullback-Leibler divergences. To illustrate the relevance of the Cram\'er distance in practice we design a new algorithm, the Cram\'er Generative Adversarial Network (GAN), and show that it performs significantly better than the related Wasserstein GAN.


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Proximal Reinforcement Learning: A New Theory of Sequential Decision Making in Primal-Dual Spaces

May 26, 2014
Sridhar Mahadevan, Bo Liu, Philip Thomas, Will Dabney, Steve Giguere, Nicholas Jacek, Ian Gemp, Ji Liu

In this paper, we set forth a new vision of reinforcement learning developed by us over the past few years, one that yields mathematically rigorous solutions to longstanding important questions that have remained unresolved: (i) how to design reliable, convergent, and robust reinforcement learning algorithms (ii) how to guarantee that reinforcement learning satisfies pre-specified "safety" guarantees, and remains in a stable region of the parameter space (iii) how to design "off-policy" temporal difference learning algorithms in a reliable and stable manner, and finally (iv) how to integrate the study of reinforcement learning into the rich theory of stochastic optimization. In this paper, we provide detailed answers to all these questions using the powerful framework of proximal operators. The key idea that emerges is the use of primal dual spaces connected through the use of a Legendre transform. This allows temporal difference updates to occur in dual spaces, allowing a variety of important technical advantages. The Legendre transform elegantly generalizes past algorithms for solving reinforcement learning problems, such as natural gradient methods, which we show relate closely to the previously unconnected framework of mirror descent methods. Equally importantly, proximal operator theory enables the systematic development of operator splitting methods that show how to safely and reliably decompose complex products of gradients that occur in recent variants of gradient-based temporal difference learning. This key technical innovation makes it possible to finally design "true" stochastic gradient methods for reinforcement learning. Finally, Legendre transforms enable a variety of other benefits, including modeling sparsity and domain geometry. Our work builds extensively on recent work on the convergence of saddle-point algorithms, and on the theory of monotone operators.

* 121 pages 

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Successor Features for Transfer in Reinforcement Learning

Apr 12, 2018
André Barreto, Will Dabney, Rémi Munos, Jonathan J. Hunt, Tom Schaul, Hado van Hasselt, David Silver

Transfer in reinforcement learning refers to the notion that generalization should occur not only within a task but also across tasks. We propose a transfer framework for the scenario where the reward function changes between tasks but the environment's dynamics remain the same. Our approach rests on two key ideas: "successor features", a value function representation that decouples the dynamics of the environment from the rewards, and "generalized policy improvement", a generalization of dynamic programming's policy improvement operation that considers a set of policies rather than a single one. Put together, the two ideas lead to an approach that integrates seamlessly within the reinforcement learning framework and allows the free exchange of information across tasks. The proposed method also provides performance guarantees for the transferred policy even before any learning has taken place. We derive two theorems that set our approach in firm theoretical ground and present experiments that show that it successfully promotes transfer in practice, significantly outperforming alternative methods in a sequence of navigation tasks and in the control of a simulated robotic arm.

* Published at NIPS 2017 

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Distributed Distributional Deterministic Policy Gradients

Apr 23, 2018
Gabriel Barth-Maron, Matthew W. Hoffman, David Budden, Will Dabney, Dan Horgan, Dhruva TB, Alistair Muldal, Nicolas Heess, Timothy Lillicrap

This work adopts the very successful distributional perspective on reinforcement learning and adapts it to the continuous control setting. We combine this within a distributed framework for off-policy learning in order to develop what we call the Distributed Distributional Deep Deterministic Policy Gradient algorithm, D4PG. We also combine this technique with a number of additional, simple improvements such as the use of $N$-step returns and prioritized experience replay. Experimentally we examine the contribution of each of these individual components, and show how they interact, as well as their combined contributions. Our results show that across a wide variety of simple control tasks, difficult manipulation tasks, and a set of hard obstacle-based locomotion tasks the D4PG algorithm achieves state of the art performance.


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Rainbow: Combining Improvements in Deep Reinforcement Learning

Oct 06, 2017
Matteo Hessel, Joseph Modayil, Hado van Hasselt, Tom Schaul, Georg Ostrovski, Will Dabney, Dan Horgan, Bilal Piot, Mohammad Azar, David Silver

The deep reinforcement learning community has made several independent improvements to the DQN algorithm. However, it is unclear which of these extensions are complementary and can be fruitfully combined. This paper examines six extensions to the DQN algorithm and empirically studies their combination. Our experiments show that the combination provides state-of-the-art performance on the Atari 2600 benchmark, both in terms of data efficiency and final performance. We also provide results from a detailed ablation study that shows the contribution of each component to overall performance.

* Under review as a conference paper at AAAI 2018 

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A Geometric Perspective on Optimal Representations for Reinforcement Learning

Jan 31, 2019
Marc G. Bellemare, Will Dabney, Robert Dadashi, Adrien Ali Taiga, Pablo Samuel Castro, Nicolas Le Roux, Dale Schuurmans, Tor Lattimore, Clare Lyle

This paper proposes a new approach to representation learning based on geometric properties of the space of value functions. We study a two-part approximation of the value function: a nonlinear map from states to vectors, or representation, followed by a linear map from vectors to values. Our formulation considers adapting the representation to minimize the (linear) approximation of the value function of all stationary policies for a given environment. We show that this optimization reduces to making accurate predictions regarding a special class of value functions which we call adversarial value functions (AVFs). We argue that these AVFs make excellent auxiliary tasks, and use them to construct a loss which can be efficiently minimized to find a near-optimal representation for reinforcement learning. We highlight characteristics of the method in a series of experiments on the four-room domain.


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