Symmetric Mean-field Langevin Dynamics for Distributional Minimax Problems

arXiv:2312.01127v2 Announce Type: replace-cross
Abstract: 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 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 …

abstract algorithm arxiv distribution dynamics gradient loop math.oc mean minimax novel optimization paper probability spaces stat.ml type updates