mlsanityData to 14 Oct 2026

Convergence of two-timescale gradient descent ascent dynamics: finite-dimensional and mean-field perspectives

arXiv 2501.17122 ↗First posted 28 Jan 2025math.OC cs.LG cs.NAcited by 2

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Abstract (arXiv)

The two-timescale gradient descent-ascent (GDA) is a canonical gradient algorithm designed to find Nash equilibria in min-max games. We analyze the two-timescale GDA by investigating the effects of learning rate ratios on convergence behavior in both finite-dimensional and mean-field settings. In particular, for finite-dimensional quadratic min-max games, we obtain long-time convergence in near quasi-static regimes through the hypocoercivity method. For mean-field GDA dynamics, we investigate convergence under a finite-scale ratio using a mixed synchronous-reflection coupling technique.

Key facts. Cited by 2 papers in the map (data through 14 Oct 2026). Builds on 27 of its 55 references that are in the map. First posted on arXiv 28 Jan 2025.

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27 of 55 references.

References · 27

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15 more
  1. 2017Communication-Efficient Algorithms for Decentralized and Stochastic Optimizationcited by 43
  2. 2019Differentiable Game Mechanicscited by 43
  3. 2019Improved Bounds for Discretization of Langevin Diffusions: Near-Optimal Rates without Convexitycited by 39
  4. 2019A Tale of Two-Timescale Reinforcement Learning with the Tightest Finite-Time Boundcited by 31
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  10. 2022Two-Scale Gradient Descent Ascent Dynamics Finds Mixed Nash Equilibria of Continuous Games: A Mean-Field Perspectivecited by 13
  11. 2023Symmetric Mean-field Langevin Dynamics for Distributional Minimax Problemscited by 11
  12. 2021Convergence Rates of Two-Time-Scale Gradient Descent-Ascent Dynamics for Solving Nonconvex Min-Max Problemscited by 10
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  15. 2024On the Convergence of Min-Max Langevin Dynamics and Algorithmcited by 3

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Citing papers per year: 2025: 2.

2 papers.

  1. 2025Convergence of Time-Averaged Mean Field Gradient Descent Dynamics for Continuous Multi-Player Zero-Sum Gamescited by 2
  2. 2025Non-convex entropic mean-field optimization via Best Response flowcited by 2