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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…

Machine Learning · Computer Science 2017-07-24 Marc G. Bellemare , Will Dabney , Rémi Munos

Reinforcement learning is typically treated as a uniform, data-driven optimization process, where updates are guided by rewards and temporal-difference errors without explicitly exploiting global structure. In contrast, dynamic programming…

Machine Learning · Computer Science 2026-04-21 Ivo Nowak

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…

Artificial Intelligence · Computer Science 2017-10-30 Will Dabney , Mark Rowland , Marc G. Bellemare , Rémi Munos

Distributional reinforcement learning (DRL) enhances the understanding of the effects of the randomness in the environment by letting agents learn the distribution of a random return, rather than its expected value as in standard…

Optimization and Control · Mathematics 2024-03-26 Zifan Wang , Yulong Gao , Siyi Wang , Michael M. Zavlanos , Alessandro Abate , Karl H. Johansson

Diffusion models surpass previous generative models in sample quality and training stability. Recent works have shown the advantages of diffusion models in improving reinforcement learning (RL) solutions. This survey aims to provide an…

Machine Learning · Computer Science 2024-02-26 Zhengbang Zhu , Hanye Zhao , Haoran He , Yichao Zhong , Shenyu Zhang , Haoquan Guo , Tingting Chen , Weinan Zhang

Reinforcement learning (RL) struggles to scale to large, combinatorial action spaces common in many real-world problems. This paper introduces a novel framework for training discrete diffusion models as highly effective policies in these…

Machine Learning · Computer Science 2026-05-21 Haitong Ma , Ofir Nabati , Aviv Rosenberg , Bo Dai , Oran Lang , Craig Boutilier , Na Li , Shie Mannor , Lior Shani , Guy Tenneholtz

Distributional reinforcement learning (DRL) enhances the understanding of the effects of the randomness in the environment by letting agents learn the distribution of a random return, rather than its expected value as in standard RL. At the…

Optimization and Control · Mathematics 2023-03-27 Zifan Wang , Yulong Gao , Siyi Wang , Michael M. Zavlanos , Alessandro Abate , Karl H. Johansson

Reinforcement learning (RL) allows an agent interacting sequentially with an environment to maximize its long-term expected return. In the distributional RL (DistrRL) paradigm, the agent goes beyond the limit of the expected value, to…

Machine Learning · Computer Science 2023-05-01 Mastane Achab , Reda Alami , Yasser Abdelaziz Dahou Djilali , Kirill Fedyanin , Eric Moulines

Reinforcement learning (RL) has a rich history in neuroscience, from early work on dopamine as a reward prediction error signal (Schultz et al., 1997) to recent work proposing that the brain could implement a form of 'distributional…

Neurons and Cognition · Quantitative Biology 2024-12-19 Kristopher T. Jensen

In offline reinforcement learning (RL), we seek to utilize offline data to evaluate (or learn) policies in scenarios where the data are collected from a distribution that substantially differs from that of the target policy to be evaluated.…

Machine Learning · Computer Science 2021-03-09 Ruosong Wang , Yifan Wu , Ruslan Salakhutdinov , Sham M. Kakade

Classical reinforcement learning (RL) techniques are generally concerned with the design of decision-making policies driven by the maximisation of the expected outcome. Nevertheless, this approach does not take into consideration the…

Machine Learning · Computer Science 2023-01-02 Thibaut Théate , Damien Ernst

The standard reinforcement learning (RL) formulation considers the expectation of the (discounted) cumulative reward. This is limiting in applications where we are concerned with not only the expected performance, but also the distribution…

Machine Learning · Computer Science 2019-06-13 Changjian Li , Krzysztof Czarnecki

This tutorial provides a comprehensive survey of methods for fine-tuning diffusion models to optimize downstream reward functions. While diffusion models are widely known to provide excellent generative modeling capability, practical…

Machine Learning · Computer Science 2024-07-19 Masatoshi Uehara , Yulai Zhao , Tommaso Biancalani , Sergey Levine

In contrast to classical reinforcement learning (RL), distributional RL algorithms aim to learn the distribution of returns rather than their expected value. Since the nature of the return distribution is generally unknown a priori or…

Machine Learning · Computer Science 2025-03-17 Moritz A. Zanger , Wendelin Böhmer , Matthijs T. J. Spaan

We consider the problem of learning a set of probability distributions from the empirical Bellman dynamics in distributional reinforcement learning (RL), a class of state-of-the-art methods that estimate the distribution, as opposed to only…

Machine Learning · Computer Science 2020-12-10 Thanh Tang Nguyen , Sunil Gupta , Svetha Venkatesh

Distributional reinforcement learning (RL) has proven useful in multiple benchmarks as it enables approximating the full distribution of returns and extracts rich feedback from environment samples. The commonly used quantile regression…

Machine Learning · Computer Science 2025-05-27 Sami Jullien , Romain Deffayet , Jean-Michel Renders , Paul Groth , Maarten de Rijke

Distributionally robust reinforcement learning (DRRL) focuses on designing policies that achieve good performance under model uncertainties. The goal is to maximize the worst-case long-term discounted reward, where the data for RL comes…

Machine Learning · Computer Science 2026-03-17 Saptarshi Mandal , Yashaswini Murthy , R. Srikant

We propose a distributional framework for offline Inverse Reinforcement Learning (IRL) that jointly models uncertainty over reward functions and full distributions of returns. Unlike conventional IRL approaches that recover a deterministic…

Machine Learning · Computer Science 2026-05-29 Feiyang Wu , Ye Zhao , Anqi Wu

This paper studies tabular reinforcement learning (RL) in the hybrid setting, which assumes access to both an offline dataset and online interactions with the unknown environment. A central question boils down to how to efficiently utilize…

Machine Learning · Computer Science 2023-05-18 Gen Li , Wenhao Zhan , Jason D. Lee , Yuejie Chi , Yuxin Chen

Why do reinforcement learning (RL) policies fail or succeed? This is a challenging question due to the complex, high-dimensional nature of agent-environment interactions. In this work, we take a causal perspective on explaining the behavior…

Machine Learning · Statistics 2025-07-22 Armin Kekić , Jan Schneider , Dieter Büchler , Bernhard Schölkopf , Michel Besserve