English

A Fisher-Rao gradient flow for entropic mean-field min-max games

Optimization and Control 2024-09-19 v2 Machine Learning Probability

Abstract

Gradient flows play a substantial role in addressing many machine learning problems. We examine the convergence in continuous-time of a \textit{Fisher-Rao} (Mean-Field Birth-Death) gradient flow in the context of solving convex-concave min-max games with entropy regularization. We propose appropriate Lyapunov functions to demonstrate convergence with explicit rates to the unique mixed Nash equilibrium.

Keywords

Cite

@article{arxiv.2405.15834,
  title  = {A Fisher-Rao gradient flow for entropic mean-field min-max games},
  author = {Razvan-Andrei Lascu and Mateusz B. Majka and Łukasz Szpruch},
  journal= {arXiv preprint arXiv:2405.15834},
  year   = {2024}
}

Comments

24 pages. arXiv admin note: text overlap with arXiv:2306.03033