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

29 Sept 2021, 00:33 (edited 15 Feb 2022)ICLR 2022 PosterReaders: Everyone
• Keywords: quasistatic, minimax optimization, mixed Nash equilibrium, mean-field formulation
• Abstract: In this paper, we study the problem of finding 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. Theoretical analysis are conducted on this dynamics, showing its convergence to the mixed Nash equilibrium 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 GANs.
• One-sentence Summary: We propose a quasistatic Wasserstein flow for finding mixed Nash equilibriums, and prove its convergence.
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