mlsanityData to 7 Oct 2026

Provably convergent quasistatic dynamics for mean-field two-player zero-sum games

arXiv 2202.10947 ↗First posted 15 Feb 2022cs.GT cs.AI cs.LGcited by 9

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Abstract (arXiv)

In this paper, we study the problem of finding mixed Nash equilibrium for mean-field two-player zero-sum games. Solving this problem requires optimizing over two probability distributions. We consider a quasistatic Wasserstein gradient flow dynamics in which one probability distribution follows the Wasserstein gradient flow, while the other one is always at the equilibrium. Theoretical analysis are conducted on this dynamics, showing its convergence to the mixed Nash equilibrium under mild conditions. Inspired by the continuous dynamics of probability distributions, we derive a quasistatic Langevin gradient descent method with inner-outer iterations, and test the method on different problems, including training mixture of GANs.

Key facts. Cited by 9 papers in the map (data through 7 Oct 2026). Builds on 19 of its 33 references that are in the map. First posted on arXiv 15 Feb 2022.

Builds on

19 of 33 references.

References · 19

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7 more
  1. 2019Mean Field Limit of the Learning Dynamics of Multilayer Neural Networkscited by 25
  2. 2019Global convergence of neuron birth-death dynamicscited by 22
  3. 2021Wasserstein Proximal of GANscited by 15
  4. 2017An Online Learning Approach to Generative Adversarial Networkscited by 13
  5. 2019Kernelized Wasserstein Natural Gradientcited by 12
  6. 2022Simultaneous Transport Evolution for Minimax Equilibria on Measurescited by 2
  7. 2020Entropy dissipation via Information Gamma calculus: Non-reversible stochastic differential equationscited by 1

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Cited by year (2026 to 7 Oct)

Citing papers per year: 2022: 2; 2023: 3; 2024: 1; 2025: 2; 2026: 1.

9 papers.

  1. 2022An Exponentially Converging Particle Method for the Mixed Nash Equilibrium of Continuous Gamescited by 14
  2. 2022Two-Scale Gradient Descent Ascent Dynamics Finds Mixed Nash Equilibria of Continuous Games: A Mean-Field Perspectivecited by 13
  3. 2023Symmetric Mean-field Langevin Dynamics for Distributional Minimax Problemscited by 11
  4. 2024A Fisher-Rao gradient flow for entropic mean-field min-max gamescited by 3
  5. 2023PAPAL: A Provable PArticle-based Primal-Dual ALgorithm for Mixed Nash Equilibriumcited by 2
  6. 2025Convergence of two-timescale gradient descent ascent dynamics: finite-dimensional and mean-field perspectivescited by 2
  7. 2025Convergence of Time-Averaged Mean Field Gradient Descent Dynamics for Continuous Multi-Player Zero-Sum Gamescited by 2
  8. 2023Towards Optimal Randomized Strategies in Adversarial Example Gamecited by 0
  9. 2026Local exponential stability of mean-field Langevin descent-ascent and associated particle systemcited by 0