Entropic Mean-Field Min–Max Problems via Best Response Flow

Abstract We investigate the convergence properties of a continuous-time optimization method, the 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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Publication Details

Journal
Applied Mathematics & Optimization
Published
2025-03-09
DOI
https://doi.org/10.1007/s00245-025-10246-6
Primary Topic
Simulation Techniques and Applications
Type
article
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article

Entropic Mean-Field Min–Max Problems via Best Response Flow

Łukasz Szpruch, Mateusz B. Majka, Razvan-Andrei Lascu
Applied Mathematics & Optimization
Simulation Techniques and Applications
article

Entropic Mean-Field Min–Max Problems via Best Response Flow

Łukasz Szpruch, Mateusz B. Majka, Razvan-Andrei Lascu
article en

Abstract

Abstract We investigate the convergence properties of a continuous-time optimization method, the 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.

Applied Mathematics & OptimizationVol. 91(2)
Turing Institute (GB), Heriot-Watt University (GB), Maxwell Institute for Mathematical Sciences (GB), The Alan Turing Institute (GB), University of Edinburgh (GB)
Openalex Percentile: Top 95%
Simulation Techniques and Applications
DOIOpen Access PDFOpenAlex
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Entropic Mean-Field Min–Max Problems via Best Response Flow — Łukasz Szpruch, Mateusz B. Majka, et al. · Applied Mathematics & Optimization (2025) | TGRS Research Map | TGRS