Bellman Unbiasedness: Toward Provably Efficient Distributional Reinforcement Learning with General Value Function Approximation

Abstract

Distributional reinforcement learning improves performance by capturing environmental stochasticity, but a comprehensive theoretical understanding of its effectiveness remains elusive. In addition, the intractable element of the infinite dimensionality of distributions has been overlooked. In this paper, we present a regret analysis of distributional reinforcement learning with general value function approximation in a finite episodic Markov decision process setting. We first introduce a key notion of Bellman unbiasedness which is essential for exactly learnable and provably efficient distributional updates in an online manner. Among all types of statistical functionals for representing infinite-dimensional return distributions, our theoretical results demonstrate that only moment functionals can exactly capture the statistical information. Secondly, we propose a provably efficient algorithm, SF-LSVI, that achieves a tight regret bound of O(d_E H^32K) where H is the horizon, K is the number of episodes, and d_E is the eluder dimension of a function class.

Tasks

Reproductions