Almost Sure Convergence to Approximate Nash Equilibrium in Zero-Sum Extensive-Form Games with Noisy Feedback

This paper proposes a regularized optimistic gra-dient descent-ascent algorithm to seek an approximate Nash equilibrium for zero-sum extensive-form games in noisy feed-back setting, where each player only observes noisy gradients. Using a regularization technique, we establish the convergence properties of the proposed algorithm under mild assumptions. We prove that, in a noisy feedback setting, the proposed algorithm almost surely converges to an approximate Nash equilibrium, with the quality of the approximation depending on the chosen regularization parameter. Finally, we demonstrate the efficacy of the proposed algorithm through simulations on two representative extensive-form games.