Provably convergent quasistatic dynamics for mean-field two-player zero-sum games

In this talk, we study the minimax problem arising from finding the mixed Nash equilibrium for mean-field two-player zero-sum games. Solving this problem requires optimizing over two probability distributions. We consider a quasistatic Wasserstein gradient flow dynamics in which one probability distribution follows the Wasserstein gradient flow, while the other one is always at the equilibrium. The convergence of the quasistatic dynamics to the mixed Nash equilibrium is shown under mild conditions. Inspired by the continuous dynamics of probability distributions, we derive a quasistatic Langevin gradient descent method with inner-outer iterations, and test the method on different problems, including training mixture of Generative Adversarial Networks (GANs).