A Scenario Approach to the Robustness of Nonconvex-Nonconcave Minimax Problems
Fuente:
arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2025
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| Acceso en línea: | |
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| _version_ | 1866913121060257792 |
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| author | Peng, Huan Chen, Guanpu Johansson, Karl Henrik |
| author_facet | Peng, Huan Chen, Guanpu Johansson, Karl Henrik |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_15606 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A Scenario Approach to the Robustness of Nonconvex-Nonconcave Minimax Problems Peng, Huan Chen, Guanpu Johansson, Karl Henrik Computer Science and Game Theory Optimization and Control 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. |
| title | A Scenario Approach to the Robustness of Nonconvex-Nonconcave Minimax Problems |
| topic | Computer Science and Game Theory Optimization and Control |
| url | https://arxiv.org/abs/2511.15606 |