Since its introduction, the reward prediction error (RPE) theory of dopamine has explained a wealth of empirical phenomena, providing a unifying framework for understanding the representation of reward and value in the brain 1-3 . According to the now canonical theory, reward predictions are represented as a single scalar quantity, which supports learning about the expectation, or mean, of stochastic outcomes. In the present work, we propose a novel account of dopamine-based reinforcement learning. Inspired by recent artificial intelligence research on distributional reinforcement learning 4-6 , we hypothesized that the brain represents possible future rewards not as a single mean, but instead as a probability distribution, effectively representing multiple future outcomes simultaneously and in parallel. This idea leads immediately to a set of empirical predictions, which we tested using single-unit recordings from mouse ventral tegmental area. Our findings provide strong evidence for a neural realization of distributional reinforcement learning.The RPE theory of dopamine derives from work in the artificial intelligence (AI) field of reinforcement learning (RL) 7 . Since the link to neuroscience was first made, however, RL has made substantial advances 8,9 , revealing factors that radically enhance the effectiveness of RL algorithms 10 . In some cases, the relevant mechanisms invite comparison with neural function, suggesting new hypotheses concerning reward-based learning in the brain [11][12][13] . Here, we examine one particularly promising recent development in AI research and

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.

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In reinforcement learning (RL), 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.

The emergence of powerful artificial intelligence is defining new research directions in neuroscience. To date, this research has focused largely on deep neural networks trained using supervised learning, in tasks such as image classification. However, there is another area of recent AI work which has so far received less attention from neuroscientists, but which may have profound neuroscientific implications: deep reinforcement learning. Deep RL offers a comprehensive framework for studying the interplay among learning, representation and decision-making, offering to the brain sciences a new set of research tools and a wide range of novel hypotheses. In the present review, we provide a high-level introduction to deep RL, discuss some of its initial applications to neuroscience, and survey its wider implications for research on brain and behavior, concluding with a list of opportunities for next-stage research.

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