An Improved Finite-time Analysis of Temporal Difference Learning with Deep Neural Networks

TL;DR

This paper provides a new finite-time analysis of neural TD learning, achieving an improved sample complexity of  under Markovian sampling, advancing theoretical understanding of neural network-based reinforcement learning.

Contribution

It introduces novel proof techniques and derives the first finite-time analysis with  complexity for neural TD under Markovian sampling.

Findings

Achieves  sample complexity for neural TD.

Develops new proof techniques for non-asymptotic analysis.

First finite-time analysis of neural TD with Markovian sampling.

Abstract

Temporal difference (TD) learning algorithms with neural network function parameterization have well-established empirical success in many practical large-scale reinforcement learning tasks. However, theoretical understanding of these algorithms remains challenging due to the nonlinearity of the action-value approximation. In this paper, we develop an improved non-asymptotic analysis of the neural TD method with a general $L$-layer neural network. New proof techniques are developed and an improved new $\tilde{\mathcal{O}}(\epsilon^{-1})$ sample complexity is derived. To our best knowledge, this is the first finite-time analysis of neural TD that achieves an $\tilde{\mathcal{O}}(\epsilon^{-1})$ complexity under the Markovian sampling, as opposed to the best known $\tilde{\mathcal{O}}(\epsilon^{-2})$ complexity in the existing literature.