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

Razvan-Andrei Lascu; Mateusz B. Majka; Łukasz Szpruch

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arXiv · 2405.15834

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

Razvan-Andrei Lascu·Mateusz B. Majka·Łukasz Szpruch

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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.

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BibTeX RIS

Razvan-Andrei Lascu, Mateusz B. Majka, Łukasz Szpruch. 2024-05-24. A Fisher-Rao gradient flow for entropic mean-field min-max games. https://arxiv.org/abs/2405.15834

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