Near-Optimal Algorithms for Making the Gradient Small in Stochastic Minimax Optimization

We study the problem of finding a near-stationary point for smooth minimax optimization. The recently proposed extra anchored gradient (EAG) methods achieve the optimal convergence rate for the convex-concave minimax problem in the deterministic setting. However, the direct extension of EAG to stochastic optimization is not efficient. In this paper, we design a novel stochastic algorithm called Recursive Anchored IteratioN (RAIN). We show that the RAIN achieves near-optimal stochastic first-order oracle (SFO) complexity for stochastic minimax optimization in both convex-concave and strongly-convex-strongly-concave cases. In addition, we extend the idea of RAIN to solve structured nonconvex-nonconcave minimax problem and it also achieves near-optimal SFO complexity.

@article{chen2025_2208.05925,
  title={ Near-Optimal Algorithms for Making the Gradient Small in Stochastic Minimax Optimization },
  author={ Lesi Chen and Luo Luo },
  journal={arXiv preprint arXiv:2208.05925},
  year={ 2025 }
}