An Efficient Stochastic Algorithm for Decentralized Nonconvex-Strongly-Concave Minimax Optimization

@InProceedings{pmlr-v238-chen24b,
  title = 	 {An Efficient Stochastic Algorithm for Decentralized Nonconvex-Strongly-Concave Minimax Optimization},
  author =       {Chen, Lesi and Ye, Haishan and Luo, Luo},
  booktitle = 	 {Proceedings of The 27th International Conference on Artificial Intelligence and Statistics},
  pages = 	 {1990--1998},
  year = 	 {2024},
  editor = 	 {Dasgupta, Sanjoy and Mandt, Stephan and Li, Yingzhen},
  volume = 	 {238},
  series = 	 {Proceedings of Machine Learning Research},
  month = 	 {02--04 May},
  publisher =    {PMLR},
  pdf = 	 {https://proceedings.mlr.press/v238/chen24b/chen24b.pdf},
  url = 	 {https://proceedings.mlr.press/v238/chen24b.html},
  abstract = 	 {This paper studies the stochastic nonconvex-strongly-concave minimax optimization over a multi-agent network. We propose an efficient algorithm, called Decentralized Recursive gradient descEnt Ascent Method (DREAM), which achieves the best-known theoretical guarantee for finding the $\epsilon$-stationary points. Concretely, it requires $\mathcal{O}(\min (\kappa^3\epsilon^{-3},\kappa^2 \sqrt{N} \epsilon^{-2} ))$ stochastic first-order oracle (SFO) calls and $\tilde \mathcal O(\kappa^2 \epsilon^{-2})$ communication rounds, where $\kappa$ is the condition number and $N$ is the total number of individual functions. Our numerical experiments also validate the superiority of DREAM over previous methods.}
}