  In this paper, we introduce a regularized mean-field game and study learning
of this game under an infinite-horizon discounted reward function.
Regularization is introduced by adding a strongly concave 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. The regularization term in
general makes reinforcement learning algorithm more robust to the system
components. 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.
