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The distributional reinforcement learning (RL) approach advocates for representing the complete probability distribution of the random return instead of only modelling its expectation. A distributional RL algorithm may be characterised by…

Machine Learning · Computer Science 2023-03-20 Thibaut Théate , Antoine Wehenkel , Adrien Bolland , Gilles Louppe , Damien Ernst

To date, distributional reinforcement learning (distributional RL) methods have exclusively focused on the discounted setting, where an agent aims to optimize a discounted sum of rewards over time. In this work, we extend distributional RL…

Machine Learning · Computer Science 2026-01-14 Juan Sebastian Rojas , Chi-Guhn Lee

Distributional Reinforcement Learning (RL) differs from traditional RL in that, rather than the expectation of total returns, it estimates distributions and has achieved state-of-the-art performance on Atari Games. The key challenge in…

Machine Learning · Computer Science 2020-08-04 Derek Yang , Li Zhao , Zichuan Lin , Tao Qin , Jiang Bian , Tieyan Liu

In the regression problem, L1 and L2 are the most commonly used loss functions, which produce mean predictions with different biases. However, the predictions are neither robust nor adequate enough since they only capture a few conditional…

Machine Learning · Computer Science 2019-11-14 Faen Zhang , Xinyu Fan , Hui Xu , Pengcheng Zhou , Yujian He , Junlong Liu

Distributional reinforcement learning, which focuses on learning the entire return distribution instead of only its expectation in standard RL, has demonstrated remarkable success in enhancing performance. Despite these advancements, our…

Machine Learning · Computer Science 2024-09-24 Ke Sun , Bei Jiang , Linglong Kong

In distributional reinforcement learning (RL), the estimated distribution of value function models both the parametric and intrinsic uncertainties. We propose a novel and efficient exploration method for deep RL that has two components. The…

Machine Learning · Computer Science 2019-05-16 Borislav Mavrin , Shangtong Zhang , Hengshuai Yao , Linglong Kong , Kaiwen Wu , Yaoliang Yu

The recently proposed distributional approach to reinforcement learning (DiRL) is centered on learning the distribution of the reward-to-go, often referred to as the value distribution. In this work, we show that the distributional Bellman…

Machine Learning · Computer Science 2018-08-07 Dror Freirich , Ron Meir , Aviv Tamar

Average-reward reinforcement learning requires estimating the gain and the bias, which is defined only up to an additive constant. This makes direct distributional analogues ill-posed on the real line. We introduce a quotient-space…

Machine Learning · Computer Science 2026-05-13 Ege C. Kaya , Aliasghar Pourghani , Vijay Gupta , Abolfazl Hashemi

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

Distributional reinforcement learning (DRL) studies the evolution of full return distributions under Bellman updates rather than focusing on expected values. A classical result is that the distributional Bellman operator is contractive…

Machine Learning · Computer Science 2026-03-16 Keru Wang , Yixin Deng , Yao Lyu , Stephen Redmond , Shengbo Eben Li

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

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…

Machine Learning · Computer Science 2018-06-20 Will Dabney , Georg Ostrovski , David Silver , Rémi Munos

Meta-reinforcement learning algorithms provide a data-driven way to acquire policies that quickly adapt to many tasks with varying rewards or dynamics functions. However, learned meta-policies are often effective only on the exact task…

Machine Learning · Computer Science 2023-07-13 Anurag Ajay , Abhishek Gupta , Dibya Ghosh , Sergey Levine , Pulkit Agrawal

Mainstream approximate action-value iteration reinforcement learning (RL) algorithms suffer from overestimation bias, leading to suboptimal policies in high-variance stochastic environments. Quantile-based action-value iteration methods…

Machine Learning · Computer Science 2025-12-09 Clinton Enwerem , Aniruddh G. Puranic , John S. Baras , Calin Belta

Regularization schemes for regression have been widely studied in learning theory and inverse problems. In this paper, we study distribution regression (DR) which involves two stages of sampling, and aims at regressing from probability…

Machine Learning · Computer Science 2021-10-27 Zhan Yu , Daniel W. C. Ho , Ding-Xuan Zhou

We propose a novel one-step supervised imitation learning (IL) framework called Adversarial Density Regression (ADR). This IL framework aims to correct the policy learned on unknown-quality to match the expert distribution by utilizing…

Machine Learning · Computer Science 2025-01-14 Ziqi Zhang , Zifeng Zhuang , Jingzehua Xu , Yiyuan Yang , Yubo Huang , Donglin Wang , Shuai Zhang

We describe a new approach for managing aleatoric uncertainty in the Reinforcement Learning (RL) paradigm. Instead of selecting actions according to a single statistic, we propose a distributional method based on the second-order stochastic…

Machine Learning · Computer Science 2020-10-08 John D. Martin , Michal Lyskawinski , Xiaohu Li , Brendan Englot

Chaotic dynamical systems pose a fundamental challenge for Reinforcement Learning (RL): exponential sensitivity to initial conditions induces high-variance bootstrap targets and poorly conditioned gradient updates. Chaotic dynamics arise…

Machine Learning · Computer Science 2026-05-29 James Rudd-Jones , Mirco Musolesi , María Pérez-Ortiz

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

Designing model-free algorithms for distributionally robust reinforcement learning (DRRL) poses fundamental challenges. The robust Bellman operator is nonlinear in the transition kernel, which makes one-sample Bellman updates biased, while…

Machine Learning · Computer Science 2026-05-12 Shengbo Wang , Zexi Zhang