Q-Learning in Regularized Mean-field Games

In this paper, we introduce a regularized mean-field game and study learning of this game under an infinite-horizon discounted reward function. The game is defined by adding a regularization function to the one-stage reward function in the classical mean-field game model. We establish a value iteration based learning algorithm to this regularized mean-field game using fitted Q-learning. This regularization term in general makes reinforcement learning algorithm more robust with improved exploration. Moreover, it enables us to establish error analysis of the learning algorithm without imposing restrictive convexity assumptions on the system components, which are needed in the absence of a regularization term.