On the Global Convergence of Fitted Q-Iteration with Two-layer Neural Network Parametrization

TL;DR

This paper provides theoretical guarantees for a Fitted Q-Iteration algorithm using two-layer neural networks, demonstrating it achieves near-optimal sample complexity without restrictive assumptions.

Contribution

It establishes the first sample complexity bounds for neural network-based Fitted Q-Iteration in general MDPs without linearity assumptions.

Findings

Achieves $ ilde{O}(1/\epsilon^2)$ sample complexity

Works for countable state spaces without structural assumptions

Provides convergence guarantees for neural network parametrization

Abstract

Deep Q-learning based algorithms have been applied successfully in many decision making problems, while their theoretical foundations are not as well understood. In this paper, we study a Fitted Q-Iteration with two-layer ReLU neural network parameterization, and find the sample complexity guarantees for the algorithm. Our approach estimates the Q-function in each iteration using a convex optimization problem. We show that this approach achieves a sample complexity of $\tilde{\mathcal{O}}(1/\epsilon^{2})$, which is order-optimal. This result holds for a countable state-spaces and does not require any assumptions such as a linear or low rank structure on the MDP.