Understanding Deep Neural Function Approximation in Reinforcement Learning via ϵ-Greedy Exploration

This paper provides a theoretical study of deep neural function approximation in reinforcement learning (RL) with the ϵ-greedy exploration under the online setting. This problem setting is motivated by the successful deep Q-networks (DQN) framework that falls in this regime. In this work, we provide an initial attempt on theoretical understanding deep RL from the perspective of function class and neural networks architectures (e.g., width and depth) beyond the "linear" regime. To be specific, we focus on the value based algorithm with the ϵ-greedy exploration via deep (and two-layer) neural networks endowed by Besov (and Barron) function spaces, respectively, which aims at approximating an α-smooth Q-function in a d-dimensional feature space.