{"paper":{"title":"A Scenario Approach to the Robustness of Nonconvex-Nonconcave Minimax Problems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"The scenario approach yields a probabilistic robustness guarantee for ε-stationary points in nonconvex-nonconcave minimax problems by proving monotonicity of the stationary residual.","cross_cats":["math.OC"],"primary_cat":"cs.GT","authors_text":"Guanpu Chen, Huan Peng, Karl Henrik Johansson","submitted_at":"2025-11-19T16:53:29Z","abstract_excerpt":"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 b"},"claims":{"count":4,"items":[{"kind":"strongest_claim","text":"we first establish a probabilistic robustness guarantee for an ε-stationary point, overcoming the dependence on the non-degeneracy assumption by proving the monotonicity of the stationary residual in the number of scenarios.","source":"verdict.strongest_claim","status":"machine_extracted","claim_id":"C1","attestation":"unclaimed"},{"kind":"weakest_assumption","text":"Convex strategy sets for all players together with the standard assumptions of the scenario optimization framework from prior literature.","source":"verdict.weakest_assumption","status":"machine_extracted","claim_id":"C2","attestation":"unclaimed"},{"kind":"one_line_summary","text":"Scenario approach establishes probabilistic robustness for epsilon-stationary points in convex-strategy minimax problems via monotonicity of residuals and a relaxed bound for global points in nonconvex cases.","source":"verdict.one_line_summary","status":"machine_extracted","claim_id":"C3","attestation":"unclaimed"},{"kind":"headline","text":"The scenario approach yields a probabilistic robustness guarantee for ε-stationary points in nonconvex-nonconcave minimax problems by proving monotonicity of the stationary residual.","source":"verdict.pith_extraction.headline","status":"machine_extracted","claim_id":"C4","attestation":"unclaimed"}],"snapshot_sha256":"d787e7d4483c1dd6471b96f8441b617caaa5ea23829c7a8ef525ff2574c1a1cc"},"source":{"id":"2511.15606","kind":"arxiv","version":2},"verdict":{"id":"1009824b-670d-4ac9-b50c-341107243b4e","model_set":{"reader":"grok-4.3"},"created_at":"2026-05-17T20:28:17.304341Z","strongest_claim":"we first establish a probabilistic robustness guarantee for an ε-stationary point, overcoming the dependence on the non-degeneracy assumption by proving the monotonicity of the stationary residual in the number of scenarios.","one_line_summary":"Scenario approach establishes probabilistic robustness for epsilon-stationary points in convex-strategy minimax problems via monotonicity of residuals and a relaxed bound for global points in nonconvex cases.","pipeline_version":"pith-pipeline@v0.9.0","weakest_assumption":"Convex strategy sets for all players together with the standard assumptions of the scenario optimization framework from prior literature.","pith_extraction_headline":"The scenario approach yields a probabilistic robustness guarantee for ε-stationary points in nonconvex-nonconcave minimax problems by proving monotonicity of the stationary residual."},"references":{"count":3,"sample":[{"doi":"10.1109/tac.2025.3634219","year":2006,"title":"Aliprantis, C.D. and Border, K.C. (2006). Infinite Dimen- sional Analysis: A Hitchhiker’s Guide . Springer, 3rd edition. Assif, M., Chatterjee, D., and Banavar, R. (2020). Scenario approach for minmax ","work_id":"4e854a4c-0b6c-4c6f-b85c-7646230c3b01","ref_index":1,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":2014,"title":"Goodfellow, I., Pouget-Abadie, J., Mirza, M., Xu, B., Warde-Farley, D., Ozair, S., Courville, A., and Bengio, Y. (2014). Generative adversarial nets. In Advances in Neural Information Processing Syste","work_id":"16e6f931-9cfe-4f8d-9896-d7eeb9e03a6f","ref_index":2,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":2022,"title":"Yang, J., Orvieto, A., Lucchi, A., and He, N. (2022). Faster single-loop algorithms for minimax optimization without strong concavity. 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