Near-Minimax-Optimal Distributional Reinforcement Learning with a Generative Model

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 question of Zhang et al. (2023). Our analysis provides new theoretical results on categorical approaches to distributional RL, and also introduces a new distributional Bellman equation, the stochastic categorical CDF Bellman equation, which we expect to be of independent interest. We also provide an experimental study comparing several model-based distributional RL algorithms, with several takeaways for practitioners.