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<p>We investigate the convergence properties of a continuous-time optimization method, the <i>Mean-Field Best Response</i> 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.</p>

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

  • 期刊论文

  • 出版模式：

    开放获取

  • 发表日期：

    2025年3月9日

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  • Razvan-Andrei Lascu,
  • Mateusz B. Majka,
  • Łukasz Szpruch

摘要

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.