{"paper":{"title":"SAPD+: An Accelerated Stochastic Method for Nonconvex-Concave Minimax Problems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OC","authors_text":"Mert G\\\"urb\\\"uzbalaban, Necdet Serhat Aybat, Xuan Zhang","submitted_at":"2022-05-30T13:20:27Z","abstract_excerpt":"We propose a new stochastic method SAPD+ for solving nonconvex-concave minimax problems of the form $\\min\\max\\mathcal{L}(x,y)=f(x)+\\Phi(x,y)-g(y)$, where $f,g$ are closed convex and $\\Phi(x,y)$ is a smooth function that is weakly convex in $x$, (strongly) concave in $y$. Let $\\delta^2$ denote the variance bound for the unbiased stochastic oracle used within SAPD+ to estimate $\\nabla\\Phi$. When $\\delta>0$, for both strongly concave and merely concave settings, SAPD+ achieves the best known oracle complexities: $\\mathcal{O}\\Big(\\kappa_y\\max\\Big\\{1,\\frac{\\delta^2}{\\epsilon^2}\\Big\\}\\frac{L\\mathcal"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2205.15084","kind":"arxiv","version":4},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2205.15084/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}