{"paper":{"title":"A Stochastic GDA Method With Backtracking For Solving 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, Qiushui Xu, Xuan Zhang","submitted_at":"2024-03-12T16:43:55Z","abstract_excerpt":"We propose a stochastic GDA (gradient descent ascent) method with backtracking (SGDA-B) to solve nonconvex-concave (NCC) minimax problems of the form: $\\min_{\\mathbf{x}} \\max_y \\sum_{i=1}^N g_i(x_i)+f(\\mathbf{x},y)-h(y)$, where $h$ and $g_i$ for $i=1,\\cdots,N$ are closed, convex functions, and for some $L,\\mu\\geq 0$, $f$ is $L$-smooth and $f(\\mathbf{x},\\cdot)$ is $\\mu$-strongly concave for all $\\mathbf{x}$ in the problem domain. We consider the stochastic setting where one only has an access to an unbiased stochastic oracle of $\\nabla f$ with a finite variance bound $\\sigma^2$. While most of t"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2403.07806","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"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"}