Accelerated Distributional Temporal Difference Learning with Linear Function Approximation

TL;DR

This paper provides a detailed statistical analysis of distributional TD learning with linear function approximation, introducing variance reduction techniques to achieve tight sample complexity bounds independent of support size.

Contribution

It offers the first finite-sample analysis of distributional TD with linear approximation and develops variance reduction algorithms with support-size-independent sample complexity.

Findings

Variance reduction improves sample efficiency

Distributional TD learning complexity matches expectation learning

Supports large support sizes without increased sample complexity

Abstract

In this paper, we study the finite-sample statistical rates of distributional temporal difference (TD) learning with linear function approximation. The purpose of distributional TD learning is to estimate the return distribution of a discounted Markov decision process for a given policy. Previous works on statistical analysis of distributional TD learning focus mainly on the tabular case. We first consider the linear function approximation setting and conduct a fine-grained analysis of the linear-categorical Bellman equation. Building on this analysis, we further incorporate variance reduction techniques in our new algorithms to establish tight sample complexity bounds independent of the support size $K$ when $K$ is large. Our theoretical results imply that, when employing distributional TD learning with linear function approximation, learning the full distribution of the return function from streaming data is no more difficult than learning its expectation. This work provide new insights into the statistical efficiency of distributional reinforcement learning algorithms.