A Fisher-Rao gradient flow for entropic mean-field min-max games

Razvan-Andrei Lascu, Mateusz B. Majka, Lukasz Szpruch

Abstract: Gradient flows play a substantial role in addressing many machine learning problems. We examine the convergence in continuous-time of a 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.

Submission Length: Regular submission (no more than 12 pages of main content)

Changes Since Last Submission: Revised version incorporating the reviewers' comments.

Assigned Action Editor: ~Stephen_Becker1

Submission Number: 2723