Large deviations for interacting particle dynamics for finding mixed equilibria in zero-sum games
This provides theoretical guarantees for a method to find robust mixed equilibria in continuous minmax games, addressing a key bottleneck in machine learning applications like GANs and RL.
The paper tackles the problem of finding mixed equilibria in two-layer zero-sum games, which is important for training generative adversarial networks and reinforcement learning, by showing that an entropic regularization method using interacting particles converges with large deviation principles as particle count increases.
Finding equilibrium points in continuous minmax games has become a key problem within machine learning, in part due to its connection to the training of generative adversarial networks and reinforcement learning. Because of existence and robustness issues, recent developments have shifted from pure equilibria to focusing on mixed equilibrium points. In this work we consider a method for finding mixed equilibria in two-layer zero-sum games based on entropic regularisation, where the two competing strategies are represented by two sets of interacting particles. We show that the sequence of empirical measures of the particle system satisfies a large deviation principle as the number of particles grows to infinity, and how this implies convergence of the empirical measure and the associated Nikaidô-Isoda error, complementing existing law of large numbers results.