A Generalized Minimax Q-Learning Algorithm for Two-Player Zero-Sum Stochastic Games

We consider the problem of two-player zero-sum games. This problem is formulated as a min–max Markov game in this article. The solution of this game, which is the min–max payoff, starting from a given state is called the min–max value of the state. In this article, we compute the solution of the two-player zero-sum game, utilizing the technique of successive relaxation that has been successfully applied in this article to compute a faster value iteration algorithm in the context of Markov decision processes. We extend the concept of successive relaxation to the setting of two-player zero-sum games. We show that, under a special structure on the game, this technique facilitates faster computation of the min–max value of the states. We then derive a generalized minimax Q-learning algorithm, which computes the optimal policy when the model information is not known. Finally, we prove the convergence of the proposed generalized minimax Q-learning algorithm utilizing stochastic approximation techniques, under an assumption on the boundedness of iterates. Through experiments, we demonstrate the effectiveness of our proposed algorithm.