Two-Timescale Extragradient for Finding Local Minimax Points

Abstract

Minimax problems are notoriously challenging to optimize. However, we present that the two-timescale extragradient method can be a viable solution. By utilizing dynamical systems theory, we show that it converges to points that satisfy the second-order necessary condition of local minimax points, under mild conditions that the two-timescale gradient descent ascent fails to work. This work provably improves upon all previous results on finding local minimax points, by eliminating a crucial assumption that the Hessian with respect to the maximization variable is nondegenerate.

Cite

Text

Chae et al. "Two-Timescale Extragradient for Finding Local Minimax Points." International Conference on Learning Representations, 2024.

Markdown

[Chae et al. "Two-Timescale Extragradient for Finding Local Minimax Points." International Conference on Learning Representations, 2024.](https://mlanthology.org/iclr/2024/chae2024iclr-twotimescale/)

BibTeX

@inproceedings{chae2024iclr-twotimescale,
  title     = {{Two-Timescale Extragradient for Finding Local Minimax Points}},
  author    = {Chae, Jiseok and Kim, Kyuwon and Kim, Donghwan},
  booktitle = {International Conference on Learning Representations},
  year      = {2024},
  url       = {https://mlanthology.org/iclr/2024/chae2024iclr-twotimescale/}
}