论文标题
求解非Convex-Nonconcave Min-Max问题，表现出弱薄荷溶液
Solving Nonconvex-Nonconcave Min-Max Problems exhibiting Weak Minty Solutions
论文作者
论文摘要
我们研究了一类结构化的非convex-nonconcave min-max问题，这些问题表现出所谓的\ emph {弱薄荷}溶液，这是直到最近引入的，但能够同时捕获单调性的不同概括。我们在此设置中证明了乐观梯度方法（OGDA）的通用版本的新型收敛结果，以最佳迭代的$ 1/k $速率与最佳迭代相匹配，以最佳的平方运算符的规范（例如，外部方法）（例如）显示。此外，我们提出了EG的自适应步长版本，该版本不需要了解问题参数。
We investigate a structured class of nonconvex-nonconcave min-max problems exhibiting so-called \emph{weak Minty} solutions, a notion which was only recently introduced, but is able to simultaneously capture different generalizations of monotonicity. We prove novel convergence results for a generalized version of the optimistic gradient method (OGDA) in this setting, matching the $1/k$ rate for the best iterate in terms of the squared operator norm recently shown for the extragradient method (EG). In addition we propose an adaptive step size version of EG, which does not require knowledge of the problem parameters.
