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arXiv · 2511.15606

A Scenario Approach to the Robustness of Nonconvex-Nonconcave Minimax Problems

Huan Peng·Guanpu Chen·Karl Henrik Johansson
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Abstract

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.

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Huan Peng, Guanpu Chen, Karl Henrik Johansson. 2025-11-19. A Scenario Approach to the Robustness of Nonconvex-Nonconcave Minimax Problems. https://arxiv.org/abs/2511.15606

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