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arXiv · 2306.03033

Entropic mean-field min-max problems via Best Response flow

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

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Razvan-Andrei Lascu, Mateusz B. Majka, Łukasz Szpruch. 2023-06-05. Entropic mean-field min-max problems via Best Response flow. https://doi.org/10.1007/s00245-025-10246-6

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