发表机构
Hong Kong University of Science and Technology（香港科技大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文提出非光滑复合极小极大优化的一阶方法，含强凸-强凹与无参数变体，以$O(\epsilon^{-5/2})$复杂度找到$\epsilon$-稳定点，优于现有界。
AI 中文摘要
本文针对一类非光滑复合强凸-强凹及非凸-凹极小极大优化问题，提出了一阶方法。我们首先为强凸-强凹问题开发了一种不精确近端方法和一种累积正则化方法。后者实现了对曲率参数的最优依赖，并将较小的曲率置于精度对数之内。利用该方法作为子求解器，我们为非凸-凹问题提出了一种近端点方法。在适当假设下，该方法以$O(\epsilon^{-5/2})$的操作复杂度找到$\epsilon$-稳定点，通过去除对数因子，改进了已知最佳的$O(\epsilon^{-5/2}\log(1/\epsilon))$界。我们进一步为两类问题开发了无参数变体，在无需知晓任何问题常数的情况下实现了相同的复杂度。所有提出的方法均配备了可验证的终止准则。
英文摘要
In this paper we propose first-order methods for a class of nonsmooth composite strongly convex--strongly concave and nonconvex--concave minimax optimization. We first develop an inexact proximal method and an accumulative regularizated method for strongly convex--strongly concave problems. The latter achieves the optimal dependence on the curvature parameters and places the smaller curvature inside the accuracy logarithm. Using this method as a subsolver, we propose a proximal point method for nonconvex--concave problems. Under suitable assumptions, it finds an $ε$-stationary point with an operation complexity of $O(ε^{-5/2})$, which improves the best-known $O(ε^{-5/2}\log(1/ε))$ bounds by removing the logarithmic factor. We further develop parameter-free variants for both problem classes, and achieve the same complexity without knowledge of any problem constants. All proposed methods are equipped with verifiable termination criteria.
