Accelerated Distributional Temporal Difference Learning with Linear Function Approximation
This work provides new insights into the statistical efficiency of distributional reinforcement learning algorithms, addressing a known bottleneck in scaling to large state spaces.
The paper tackles the problem of estimating the full return distribution in reinforcement learning using distributional temporal difference learning with linear function approximation, establishing tight sample complexity bounds that are independent of support size for large K.
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.