A Differential Perspective on Distributional Reinforcement Learning

To date, distributional reinforcement learning (distributional RL) methods have exclusively focused on the discounted setting, where an agent aims to optimize a potentially-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 consistently yield competitive performance when compared to their non-distributional equivalents, while also capturing rich information about the long-run reward and return distributions.

@article{rojas2025_2506.03333,
  title={ A Differential Perspective on Distributional Reinforcement Learning },
  author={ Juan Sebastian Rojas and Chi-Guhn Lee },
  journal={arXiv preprint arXiv:2506.03333},
  year={ 2025 }
}