  We study the problem of finding a near-stationary point for smooth minimax
optimization. The recent proposed extra anchored gradient (EAG) methods achieve
the optimal convergence rate for the convex-concave minimax problem in
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.
