@inproceedings{
kim2023symmetric,
title={Symmetric Mean-field Langevin Dynamics for Distributional Minimax Problems},
author={Juno Kim and Kakei Yamamoto and Kazusato Oko and Zhuoran Yang and Taiji Suzuki},
booktitle={NeurIPS 2023 Workshop on Mathematics of Modern Machine Learning},
year={2023},
url={https://openreview.net/forum?id=eHZhjP5QdR}
}
In this paper, we extend mean-field Langevin dynamics to minimax optimization over probability distributions for the first time with symmetric and provably convergent updates. We propose \emph{mean-field Langevin averaged gradient} (MFL-AG), a single-loop algorithm that implements gradient descent ascent in the distribution spaces with a novel weighted averaging, and establish average-iterate convergence to the mixed Nash equilibrium. We also study both time and particle discretization regimes and prove a new uniform-in-time propagation of chaos result which accounts for the dependency of the particle interactions on all previous distributions. Furthermore, we propose \emph{mean-field Langevin anchored best response} (MFL-ABR), a symmetric double-loop algorithm based on best response dynamics with linear last-iterate convergence. Finally, we study applications to zero-sum Markov games and conduct simulations demonstrating long-term optimality.
Symmetric Mean-field Langevin Dynamics for Distributional Minimax Problems
Juno Kim Kakei Yamamoto Kazusato Oko Zhuoran Yang Taiji Suzuki