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A Fisher-Rao gradient flow for entropic mean-field min-max games (2405.15834v2)
Published 24 May 2024 in math.OC, cs.LG, and math.PR
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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