mlsanityData to 7 Oct 2026

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

arXiv 2405.15834 ↗First posted 24 May 2024math.OC cs.LG math.PRcited by 3

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Abstract (arXiv)

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

Key facts. Cited by 3 papers in the map (data through 7 Oct 2026). Builds on 22 of its 45 references that are in the map. First posted on arXiv 24 May 2024.

Builds on

22 of 45 references.

References · 22

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  8. 2022Mirror Descent with Relative Smoothness in Measure Spaces, with application to Sinkhorn and EMcited by 33
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  11. 2021Convergence Rates of Gradient Methods for Convex Optimization in the Space of Measurescited by 19
  12. 2022An Exponentially Converging Particle Method for the Mixed Nash Equilibrium of Continuous Gamescited by 14
10 more
  1. 2022Two-Scale Gradient Descent Ascent Dynamics Finds Mixed Nash Equilibria of Continuous Games: A Mean-Field Perspectivecited by 13
  2. 2023Symmetric Mean-field Langevin Dynamics for Distributional Minimax Problemscited by 11
  3. 2022Provably convergent quasistatic dynamics for mean-field two-player zero-sum gamescited by 9
  4. 2020Game on Random Environment, Mean-field Langevin System and Neural Networkscited by 8
  5. 2020Gradient Flows for Regularized Stochastic Control Problemscited by 8
  6. 2022Mutation-Driven Follow the Regularized Leader for Last-Iterate Convergence in Zero-Sum Gamescited by 8
  7. 2020Ergodicity of the underdamped mean-field Langevin dynamicscited by 7
  8. 2022Polyak-L ojasiewicz inequality on the space of measures and convergence of mean-field birth-death processescited by 6
  9. 2023Entropic mean-field min-max problems via Best Response flowcited by 2
  10. 2024Mirror Descent-Ascent for mean-field min-max problemscited by 1

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Cited by year (2026 to 7 Oct)

Citing papers per year: 2025: 2; 2026: 1.

3 papers.

  1. 2025Solving Inverse Problems via Diffusion-Based Priors: An Approximation-Free Ensemble Sampling Approachcited by 18
  2. 2025Non-convex entropic mean-field optimization via Best Response flowcited by 2
  3. 2026On propagation of chaos for the Fisher-Rao gradient flow in entropic mean-field optimizationcited by 0