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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

Offline reinforcement learning (RL) aims to learn an optimal policy from a static dataset, making it particularly valuable in scenarios where data collection is costly, such as robotics. A major challenge in offline RL is distributional…

Machine Learning · Computer Science 2025-07-16 Motoki Omura , Yusuke Mukuta , Kazuki Ota , Takayuki Osa , Tatsuya Harada

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

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

We introduce an innovative approach that incorporates a Distributionally Robust Learning (DRL) approach into Cox regression to enhance the robustness and accuracy of survival predictions. By formulating a DRL framework with a Wasserstein…

Machine Learning · Computer Science 2025-06-10 Yeping Jin , Lauren Wise , Ioannis Ch. Paschalidis

Aligning generative diffusion models with human preferences via reinforcement learning (RL) is critical yet challenging. Most existing algorithms are often vulnerable to reward hacking, such as quality degradation, over-stylization, or…

We propose an (offline) multi-dimensional distributional reinforcement learning framework (KE-DRL) that leverages Hilbert space mappings to estimate the kernel mean embedding of the multi-dimensional value distribution under a proposed…

Machine Learning · Computer Science 2026-01-28 Mehrdad Mohammadi , Qi Zheng , Ruoqing Zhu

Distributionally robust supervised learning (DRSL) is emerging as a key paradigm for building reliable machine learning systems for real-world applications -- reflecting the need for classifiers and predictive models that are robust to the…

Machine Learning · Computer Science 2022-01-26 Yaodong Yu , Tianyi Lin , Eric Mazumdar , Michael I. Jordan

Distributional Reinforcement Learning (RL) estimates return distribution mainly by learning quantile values via minimizing the quantile Huber loss function, entailing a threshold parameter often selected heuristically or via hyperparameter…

Machine Learning · Computer Science 2024-01-09 Parvin Malekzadeh , Konstantinos N. Plataniotis , Zissis Poulos , Zeyu Wang

Conventional off-policy reinforcement learning (RL) focuses on maximizing the expected return of scalar rewards. Distributional RL (DRL), in contrast, studies the distribution of returns with the distributional Bellman operator in a…

Machine Learning · Statistics 2024-08-15 Dong Neuck Lee , Michael R. Kosorok

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

We present a unifying framework for designing and analysing distributional reinforcement learning (DRL) algorithms in terms of recursively estimating statistics of the return distribution. Our key insight is that DRL algorithms can be…

Machine Learning · Statistics 2019-02-22 Mark Rowland , Robert Dadashi , Saurabh Kumar , Rémi Munos , Marc G. Bellemare , Will Dabney

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

Distributional approaches to value-based reinforcement learning model the entire distribution of returns, rather than just their expected values, and have recently been shown to yield state-of-the-art empirical performance. This was…

Machine Learning · Statistics 2018-02-23 Mark Rowland , Marc G. Bellemare , Will Dabney , Rémi Munos , Yee Whye Teh

Distributional Reinforcement Learning (RL) maintains the entire probability distribution of the reward-to-go, i.e. the return, providing more learning signals that account for the uncertainty associated with policy performance, which may be…

Machine Learning · Computer Science 2021-03-24 Luchen Li , A. Aldo Faisal

We study distributionally robust optimization with Sinkhorn distance -- a variant of Wasserstein distance based on entropic regularization. We derive a convex programming dual reformulation for general nominal distributions, transport…

Optimization and Control · Mathematics 2025-03-27 Jie Wang , Rui Gao , Yao Xie

Distributionally robust optimization (DRO) has emerged as a powerful paradigm for reliable decision-making under uncertainty. This paper focuses on DRO with ambiguity sets defined via the Sinkhorn discrepancy: an entropy-regularized…

Machine Learning · Statistics 2025-12-16 Jie Wang

Learning a predictive model of the mean return, or value function, plays a critical role in many reinforcement learning algorithms. Distributional reinforcement learning (DRL) has been shown to improve performance by modeling the value…

Machine Learning · Computer Science 2025-07-08 Ju-Seung Byun , Andrew Perrault

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

We propose a new algorithm for model-based distributional reinforcement learning (RL), and prove that it is minimax-optimal for approximating return distributions with a generative model (up to logarithmic factors), resolving an open…

Machine Learning · Computer Science 2024-11-05 Mark Rowland , Li Kevin Wenliang , Rémi Munos , Clare Lyle , Yunhao Tang , Will Dabney
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