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

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 parametrization, and find the sample complexity guarantees for the algorithm. The 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-space and does not require any assumptions such as a linear or low rank structure on the MDP.