On the Performance of Temporal Difference Learning With Neural Networks

Neural Temporal Difference (TD) Learning is an approximate temporal difference method for policy evaluation that uses a neural network for function approximation. Analysis of Neural TD Learning has proven to be challenging. In this paper we provide a convergence analysis of Neural TD Learning with a projection onto $B(θ_0, ω)$, a ball of fixed radius $ω$ around the initial point $θ_0$. We show an approximation bound of $O(ε) + \tilde{O} (1/\sqrt{m})$ where $ε$ is the approximation quality of the best neural network in $B(θ_0, ω)$ and $m$ is the width of all hidden layers in the network.