mlsanityData to 7 Oct 2026

Symmetric Mean-field Langevin Dynamics for Distributional Minimax Problems

arXiv 2312.01127 ↗First posted 2 Dec 2023math.OC stat.MLcited by 11

Not on the map. Why?

Abstract (arXiv)

In this paper, we extend mean-field Langevin dynamics to minimax optimization over probability distributions for the first time with symmetric and provably convergent updates. We propose mean-field Langevin averaged gradient (MFL-AG), a single-loop algorithm that implements gradient descent ascent in the distribution spaces with a novel weighted averaging, and establish average-iterate convergence to the mixed Nash equilibrium. We also study both time and particle discretization regimes and prove a new uniform-in-time propagation of chaos result which accounts for the dependency of the particle interactions on all previous distributions. Furthermore, we propose mean-field Langevin anchored best response (MFL-ABR), a symmetric double-loop algorithm based on best response dynamics with linear last-iterate convergence. Finally, we study applications to zero-sum Markov games and conduct simulations demonstrating long-term optimality.

Key facts. Cited by 11 papers in the map (data through 7 Oct 2026). Builds on 27 of its 51 references that are in the map. First posted on arXiv 2 Dec 2023.

Builds on

27 of 51 references.

References · 27

  1. 2017Towards Deep Learning Models Resistant to Adversarial Attackscited by 6,326
  2. 2022Generative Adversarial Networkscited by 5,603
  3. 2018A Mean Field View of the Landscape of Two-Layers Neural Networkscited by 463
  4. 2018On the Global Convergence of Gradient Descent for Over-parameterized Models using Optimal Transportcited by 422
  5. 2017Certifying Some Distributional Robustness with Principled Adversarial Trainingcited by 333
  6. 2018Last-Iterate Convergence: Zero-Sum Games and Constrained Min-Max Optimizationcited by 97
  7. 2021Last-iterate Convergence of Decentralized Optimistic Gradient Descent/Ascent in Infinite-horizon Competitive Markov Gamescited by 66
  8. 2022A Unified Approach to Reinforcement Learning, Quantal Response Equilibria, and Two-Player Zero-Sum Gamescited by 64
  9. 2021Fast Policy Extragradient Methods for Competitive Games with Entropy Regularizationcited by 61
  10. 2022Mean-Field Langevin Dynamics: Exponential Convergence and Annealingcited by 60
  11. 2022Convex Analysis of the Mean Field Langevin Dynamicscited by 53
  12. 2019Mean-Field Langevin Dynamics and Energy Landscape of Neural Networkscited by 49
15 more
  1. 2018Finding Mixed Nash Equilibria of Generative Adversarial Networkscited by 48
  2. 2020A mean-field analysis of two-player zero-sum gamescited by 28
  3. 2022Faster Last-iterate Convergence of Policy Optimization in Zero-Sum Markov Gamescited by 25
  4. 2022Uniform-in-time propagation of chaos for mean field Langevin dynamicscited by 23
  5. 2020Particle Dual Averaging: Optimization of Mean Field Neural Networks with Global Convergence Rate Analysiscited by 21
  6. 2020Quantitative Propagation of Chaos for SGD in Wide Neural Networkscited by 20
  7. 2022First-order Conditions for Optimization in the Wasserstein Spacecited by 19
  8. 2023Convergence of mean-field Langevin dynamics: Time and space discretization, stochastic gradient, and variance reductioncited by 19
  9. 2022Regularized Gradient Descent Ascent for Two-Player Zero-Sum Markov Gamescited by 18
  10. 2022Two-Scale Gradient Descent Ascent Dynamics Finds Mixed Nash Equilibria of Continuous Games: A Mean-Field Perspectivecited by 13
  11. 2022Entropic Fictitious Play for Mean Field Optimization Problemcited by 12
  12. 2022Provably convergent quasistatic dynamics for mean-field two-player zero-sum gamescited by 9
  13. 2020Game on Random Environment, Mean-field Langevin System and Neural Networkscited by 8
  14. 2020Revisiting SGD with Increasingly Weighted Averaging: Optimization and Generalization Perspectivescited by 3
  15. 2020Gradient Descent Averaging and Primal-dual Averaging for Strongly Convex Optimizationcited by 1

Built on by

Cited by year (2026 to 7 Oct)

Citing papers per year: 2024: 6; 2025: 4; 2026: 1.

11 papers.

  1. 2024Transformers Learn Nonlinear Features In Context: Nonconvex Mean-field Dynamics on the Attention Landscapecited by 43
  2. 2024Particle Semi-Implicit Variational Inferencecited by 7
  3. 2024Provably Neural Active Learning Succeeds via Prioritizing Perplexing Samplescited by 5
  4. 2024Analysis of Kernel Mirror Prox for Measure Optimizationcited by 4
  5. 2024A Fisher-Rao gradient flow for entropic mean-field min-max gamescited by 3
  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. 2025Non-convex entropic mean-field optimization via Best Response flowcited by 2
  9. 2024Mirror Descent-Ascent for mean-field min-max problemscited by 1
  10. 2025Iterative Sampling Methods for Sinkhorn Distributionally Robust Optimizationcited by 1
  11. 2026Local exponential stability of mean-field Langevin descent-ascent and associated particle systemcited by 0