Learning in Discrete-time Average-cost Mean-field Games

In this paper, we consider learning of discrete-time mean-field games under an average cost criterion. We propose a Q-iteration algorithm via Banach Fixed Point Theorem to compute the mean-field equilibrium when the model is known. We then extend this algorithm to the learning setting by using fitted Q-iteration and establish the probabilistic convergence of the proposed learning algorithm. Our work on learning in average-cost mean-field games appears to be the first in the literature.