{"paper":{"title":"A Single-Loop Penalty-based Algorithm for Stochastic Minimax Optimization with Nonlinear Coupled Constraints","license":"http://creativecommons.org/licenses/by/4.0/","headline":"SPACO is a single-loop stochastic gradient algorithm that solves nonconvex-concave minimax problems with nonlinear convex coupled constraints via penalty-based smoothing.","cross_cats":[],"primary_cat":"math.OC","authors_text":"Jin Zhang, Qichao Cao, Shangzhi Zeng, Yuxuan Zhou","submitted_at":"2026-05-02T04:57:02Z","abstract_excerpt":"We study stochastic nonconvex-concave minimax optimization with nonlinear\n  coupled constraints that are convex in the maximization variable. To address the nonsmoothness arising from such constraints, we develop a\n  penalty-based smooth approximation that combines quadratic penalization of the\n  coupled constraints with quadratic regularization of the inner maximization\n  problem. Based on this approximation, we propose SPACO, a single-loop\n  stochastic gradient algorithm that tracks the inner maximizer by one stochastic\n  ascent step, updates the outer variable using an inexact stochastic de"},"claims":{"count":4,"items":[{"kind":"strongest_claim","text":"We propose SPACO, a single-loop stochastic gradient algorithm built upon a penalty-based smooth approximation framework for MCC, and establish non-asymptotic complexity bounds and asymptotic stationarity of accumulation points.","source":"verdict.strongest_claim","status":"machine_extracted","claim_id":"C1","attestation":"unclaimed"},{"kind":"weakest_assumption","text":"The quadratic penalty scheme with regularization produces a continuously differentiable approximation of the MCC problem while preserving enough structure for the nonconvex-concave convergence analysis to apply.","source":"verdict.weakest_assumption","status":"machine_extracted","claim_id":"C2","attestation":"unclaimed"},{"kind":"one_line_summary","text":"SPACO is a new single-loop stochastic algorithm for stochastic nonconvex-concave minimax problems with nonlinear convex coupled constraints that uses penalty smoothing and provides non-asymptotic complexity bounds plus stationarity analysis.","source":"verdict.one_line_summary","status":"machine_extracted","claim_id":"C3","attestation":"unclaimed"},{"kind":"headline","text":"SPACO is a single-loop stochastic gradient algorithm that solves nonconvex-concave minimax problems with nonlinear convex coupled constraints via penalty-based smoothing.","source":"verdict.pith_extraction.headline","status":"machine_extracted","claim_id":"C4","attestation":"unclaimed"}],"snapshot_sha256":"5584af85e6039aab6da66c04b9114e2bd9a9fac0e3d9a67b8be6ee68957c8937"},"source":{"id":"2605.01246","kind":"arxiv","version":2},"verdict":{"id":"61fbf3ab-1717-4f1c-9bf9-bb768a3c1d31","model_set":{"reader":"grok-4.3"},"created_at":"2026-05-09T15:11:42.760267Z","strongest_claim":"We propose SPACO, a single-loop stochastic gradient algorithm built upon a penalty-based smooth approximation framework for MCC, and establish non-asymptotic complexity bounds and asymptotic stationarity of accumulation points.","one_line_summary":"SPACO is a new single-loop stochastic algorithm for stochastic nonconvex-concave minimax problems with nonlinear convex coupled constraints that uses penalty smoothing and provides non-asymptotic complexity bounds plus stationarity analysis.","pipeline_version":"pith-pipeline@v0.9.0","weakest_assumption":"The quadratic penalty scheme with regularization produces a continuously differentiable approximation of the MCC problem while preserving enough structure for the nonconvex-concave convergence analysis to apply.","pith_extraction_headline":"SPACO is a single-loop stochastic gradient algorithm that solves nonconvex-concave minimax problems with nonlinear convex coupled constraints via penalty-based smoothing."},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2605.01246/integrity.json","findings":[],"available":true,"detectors_run":[{"name":"ai_meta_artifact","ran_at":"2026-05-20T18:36:14.033711Z","status":"completed","version":"1.0.0","findings_count":0},{"name":"doi_compliance","ran_at":"2026-05-19T17:28:38.273238Z","status":"completed","version":"1.0.0","findings_count":0}],"snapshot_sha256":"328b434faf9dff3884c6319f70d7aea4fbaf12b2304868c14e09e484fb51f610"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}