Distributional Reinforcement Learning

The first comprehensive guide to distributional reinforcement learning, providing a new mathematical formalism for thinking about decisions from a probabilistic perspective.

Distributional reinforcement learning is a new mathematical formalism for thinking about decisions. Going beyond the common approach to reinforcement learning and expected values, it focuses on the total reward or return obtained as a consequence of an agent's choices—specifically, how this return behaves from a probabilistic perspective. In this first comprehensive guide to distributional reinforcement learning, Marc G. Bellemare, Will Dabney, and Mark Rowland, who spearheaded development of the field, present its key concepts and review some of its many applications. They demonstrate its power to account for many complex, interesting phenomena that arise from interactions with one's environment.

The authors present core ideas from classical reinforcement learning to contextualize distributional topics and include mathematical proofs pertaining to major results discussed in the text. They guide the reader through a series of algorithmic and mathematical developments that, in turn, characterize, compute, estimate, and make decisions on the basis of the random return. Practitioners in disciplines as diverse as finance (risk management), computational neuroscience, computational psychiatry, psychology, macroeconomics, and robotics are already using distributional reinforcement learning, paving the way for its expanding applications in mathematical finance, engineering, and the life sciences. More than a mathematical approach, distributional reinforcement learning represents a new perspective on how intelligent agents make predictions and decisions.Preface ix
1 Introduction 1
2 The Distribution of Returns 11
3 Learning the Return Distribution 51
4 Operators and Metrics 77
5 Distributional Dynamic Programming 115
6 Incremental Algorithms 161
7 Control 197
8 Statistical Functionals 233
9 Linear Function Approximation 261
10 Deep Reinforcement Learning 293
11 Two Applications and a Conclusion 319
Notation 333
References 337
Index 365“This important book extends the machinery of reinforcement learning to encompass full outcome statistics. The brain inevitably got there first, but the authors’ brilliant insights show this, how, and why.”
—Peter Dayan, Director, Max Planck Institute for Biological Cybernetics, Tübingen
 
 
“This book shows how reinforcement learning agents can estimate and use full reward distributions to make better decisions. It is a significant enhancement that opens a new range of applications.”
—Andrew Barto, Professor Emeritus, University of Massachusetts Amherst; Co-author Reinforcement Learning: An Introduction, second edition (MIT Press)Marc G. Bellemare is Senior Staff Research Scientist, Google Research and Adjunct Professor, McGill University. Will Dabney is Senior Staff Research Scientist, DeepMind. Mark Rowland is Senior Research Scientist, DeepMind.