This paper investigates probabilistic robustness of nonconvex-nonconcave minimax problems via the scenario approach. Specifically, under convex strategy sets for all players, inspired by recent advances in scenario optimization, we first establish a probabilistic robustness guarantee for an $\varepsilon$-stationary point, overcoming the dependence on the non-degeneracy assumption by proving the monotonicity of the stationary residual in the number of scenarios. Furthermore, in the presence of nonconvex strategy sets, we reveal the fundamental difficulty of obtaining a tight theoretical bound based on this recent framework. Consequently, we establish a relaxed, yet rigorously valid, probabilistic bound for a global minimax point. A numerical experiment corroborates our theoretical findings.

翻译：本文通过情景方法研究非凸-非凹极小极大问题的概率鲁棒性。具体而言，在全体玩家策略集为凸的设定下，受情景优化领域最新进展的启发，我们首先为$\varepsilon$-驻点建立了概率鲁棒性保证，通过证明驻点残差关于情景数量的单调性，克服了对非退化假设的依赖。进一步，当存在非凸策略集时，我们揭示了基于这一最新框架获得紧致理论边界的根本性困难。基于此，我们为全局极小极大点建立了一个放宽但严格有效的概率边界。数值实验验证了理论发现。