Large deviations for interacting particle dynamics for finding mixed equilibria in zero-sum games

Recent advancements in machine learning have highlighted the importance of finding equilibrium points in continuous minmax games, particularly for applications in generative adversarial networks and reinforcement learning. A novel method has been introduced that utilizes entropic regularization and models competing strategies as interacting particles. This approach shifts the focus from pure to mixed equilibria, addressing existing robustness issues. The study demonstrates that as the number of particles grows, the sequence of empirical measures adheres to a large deviation principle, leading to convergence of the empirical measure and the associated Nikaido-Isoda error. This convergence is crucial for enhancing the reliability of machine learning models, making the findings particularly relevant in the context of ongoing research in interacting particle dynamics and mixed equilibria in zero-sum games.