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 agents 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 ones 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 Distributional reinforcement learning provides a mathematical theory to describe the random outcomes caused by an agents decisions