Entropic mean-field min-max problems via Best Response flow
Optimization and Control
2025-03-11 v4 Probability
Abstract
We investigate the convergence properties of a continuous-time optimization method, the \textit{Mean-Field Best Response} flow, for solving convex-concave min-max games with entropy regularization. We introduce suitable Lyapunov functions to establish exponential convergence to the unique mixed Nash equilibrium. Additionally, we demonstrate the convergence of the fictitious play flow as a by-product of our analysis.
Keywords
Cite
@article{arxiv.2306.03033,
title = {Entropic mean-field min-max problems via Best Response flow},
author = {Razvan-Andrei Lascu and Mateusz B. Majka and Łukasz Szpruch},
journal= {arXiv preprint arXiv:2306.03033},
year = {2025}
}
Comments
34 pages, revised version, accepted for publication in Applied Mathematics & Optimization. The final manuscript is available at Springer via https://link.springer.com/article/10.1007/s00245-025-10246-6#article-info