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

Jing An, Jianfeng Lu
1/28/2025
math.OCcs.LGmath.NA

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Abstract

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.

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Cite this paper

@article{an2025convergence,
  title  = {Convergence of two-timescale gradient descent ascent dynamics: finite-dimensional and mean-field perspectives},
  author = {Jing An and Jianfeng Lu},
  year   = {2025},
  eprint = {2501.17122},
  archivePrefix = {arXiv},
  url    = {http://arxiv.org/abs/2501.17122v3}
}

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