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arXiv · 2506.03333

A Differential Perspective on Distributional Reinforcement Learning

Juan Sebastian Rojas·Chi-Guhn Lee
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Abstract

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 to the average-reward setting, where an agent aims to optimize the reward received per time step. In particular, we utilize a quantile-based approach to develop the first set of algorithms that can successfully learn and/or optimize the long-run per-step reward distribution, as well as the differential return distribution of an average-reward MDP. We derive proven-convergent tabular algorithms for both prediction and control, as well as a broader family of algorithms that have appealing scaling properties. Empirically, we find that these algorithms yield competitive and sometimes superior performance when compared to their non-distributional equivalents, while also capturing rich information about the long-run per-step reward and differential return distributions.

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Juan Sebastian Rojas, Chi-Guhn Lee. 2026-01-13. A Differential Perspective on Distributional Reinforcement Learning. https://arxiv.org/abs/2506.03333

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