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

Razvan-Andrei Lascu; Mateusz Majka; Łukasz Szpruch

doi:10.1007/s00245-025-10246-6

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

Razvan-Andrei Lascu^*, Mateusz Majka, Łukasz Szpruch

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

2 Downloads (Pure)

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.

Original language	English
Article number	48
Journal	Applied Mathematics & Optimization
Volume	91
Issue number	2
Early online date	9 Mar 2025
DOIs	https://doi.org/10.1007/s00245-025-10246-6
Publication status	Published - Apr 2025

Keywords

Best Response
Convergence rates
Entropy regularization
Fictitious play
Mean-field optimization
Mixed Nash equilibria

ASJC Scopus subject areas

Control and Optimization
Applied Mathematics

Access to Document

10.1007/s00245-025-10246-6Licence: CC BY

Download pdf
© The Author(s) 2025.
Final published version, 643 KBLicence: CC BY

Cite this

@article{0ab764a5940c4957bbb6a46506d88218,

title = "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.",

keywords = "Best Response, Convergence rates, Entropy regularization, Fictitious play, Mean-field optimization, Mixed Nash equilibria",

author = "Razvan-Andrei Lascu and Mateusz Majka and {\L}ukasz Szpruch",

year = "2025",

month = apr,

doi = "10.1007/s00245-025-10246-6",

language = "English",

volume = "91",

journal = "Applied Mathematics & Optimization",

issn = "0095-4616",

publisher = "Springer New York",

number = "2",

}

TY - JOUR

T1 - Entropic mean-field min-max problems via Best Response flow

AU - Lascu, Razvan-Andrei

AU - Majka, Mateusz

AU - Szpruch, Łukasz

PY - 2025/4

Y1 - 2025/4

N2 - 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.

AB - 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.

KW - Best Response

KW - Convergence rates

KW - Entropy regularization

KW - Fictitious play

KW - Mean-field optimization

KW - Mixed Nash equilibria

UR - http://www.scopus.com/inward/record.url?scp=86000802571&partnerID=8YFLogxK

U2 - 10.1007/s00245-025-10246-6

DO - 10.1007/s00245-025-10246-6

M3 - Article

SN - 0095-4616

VL - 91

JO - Applied Mathematics & Optimization

JF - Applied Mathematics & Optimization

IS - 2

M1 - 48

ER -

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

Abstract

Keywords

ASJC Scopus subject areas

Access to Document

Other files and links

Fingerprint

Cite this