A Fisher-Rao gradient flow for entropic mean-field min-max games
This work addresses convergence issues in min-max games for machine learning applications, but it appears incremental as it builds on existing gradient flow methods with entropy regularization.
The paper tackles the problem of solving convex-concave min-max games with entropy regularization by analyzing the convergence of a Fisher-Rao gradient flow, demonstrating explicit convergence rates to the unique mixed Nash equilibrium.
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.