On convergence rates of game theoretic reinforcement learning algorithms

This paper investigates a class of multi-player discrete games where each player aims to maximize its own utility function. Each player does not know the other players' action sets, their deployed actions or the structures of its own or the others' utility functions. Instead, each player only knows its own deployed actions and its received utility values in recent history. We propose a reinforcement learning algorithm which converges to the set of action profiles which have maximal stochastic potential with probability one. Furthermore, the convergence rate of the proposed algorithm is quantified. The algorithm performance is verified using two case studies in the smart grid and cybersecurity.