{"ID":2839649,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2511.15606","arxiv_id":"2511.15606","title":"A Scenario Approach to the Robustness of Nonconvex-Nonconcave Minimax Problems","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.","short_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 poi...","url_abs":"https://arxiv.org/abs/2511.15606","url_pdf":"https://arxiv.org/pdf/2511.15606v2","authors":"[\"Huan Peng\",\"Guanpu Chen\",\"Karl Henrik Johansson\"]","published":"2025-11-19T16:53:29Z","proceeding":"cs.GT","tasks":"[\"cs.GT\",\"math.OC\"]","methods":"[]","has_code":false}