Stochastic nonconvex minimax problems have attracted wide attention in machine learning, signal processing and many other fields in recent years. In this paper, we propose an accelerated first-order regularized momentum descent ascent algorithm (FORMDA) for solving stochastic nonconvex-concave minimax problems. The iteration complexity of the algorithm is proved to be $\tilde{\mathcal{O}}(\varepsilon ^{-6.5})$ to obtain an $\varepsilon$-stationary point, which achieves the best-known complexity bound for single-loop algorithms to solve the stochastic nonconvex-concave minimax problems under the stationarity of the objective function.

翻译：近年来，随机非凸极小极大问题在机器学习、信号处理等多个领域引起了广泛关注。本文提出了一种加速一阶正则化动量下降上升算法(FORMDA)，用于求解随机非凸-凹极小极大问题。该算法的迭代复杂度被证明为$\tilde{\mathcal{O}}(\varepsilon ^{-6.5})$，以获得$\varepsilon$-驻点，这实现了在目标函数平稳性条件下求解随机非凸-凹极小极大问题的单循环算法中已知的最佳复杂度界。