Provably convergent quasistatic dynamics for mean-field two-player zero-sum games
This work addresses a foundational challenge in game theory and machine learning for applications such as generative adversarial networks, though it appears incremental as it builds on existing gradient flow and Langevin methods.
The paper tackles the problem of finding mixed Nash equilibria in mean-field two-player zero-sum games by proposing a quasistatic Wasserstein gradient flow dynamics, proving its convergence under mild conditions, and deriving a quasistatic Langevin gradient descent method that is tested on tasks like training mixture of GANs.
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.