{"about":{"site":"https://codewithpapers.app","non_affiliation":"Code with Papers and Syntology are not affiliated with, endorsed by, or sponsored by Papers with Code, Meta, or the pwc-archive mirror.","licence":"CC BY-SA 4.0","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","attribution":"https://codewithpapers.app/attribution","modified":"archive material modified by Syntology; see the attribution page"},"url":"/paper/agda-proximal-alternating-gradient-descent","title":"AGDA+: Proximal Alternating Gradient Descent Ascent Method with a Nonmonotone Adaptive Step-Size Search for Nonconvex Minimax Problems","arxiv_id":"2406.14371","date":"2024-06-20","proceeding":null,"authors":["Xuan Zhang","Qiushui Xu","Necdet Serhat Aybat"],"abstract":"We consider double-regularized nonconvex-strongly concave (NCSC) minimax problems of the form $(P):\\min_{x\\in\\mathcal{X}} \\max_{y\\in\\mathcal{Y}}g(x)+f(x,y)-h(y)$, where $g$, $h$ are closed convex, $f$ is $L$-smooth in $(x,y)$ and strongly concave in $y$. We propose a proximal alternating gradient descent ascent method AGDA+ that can adaptively choose nonmonotone primal-dual stepsizes to compute an approximate stationary point for $(P)$ without requiring the knowledge of the global Lipschitz constant $L$ and the concavity modulus $\\mu$. Using a nonmonotone step-size search (backtracking) scheme, AGDA+ stands out by its ability to exploit the local Lipschitz structure and eliminates the need for precise tuning of hyper-parameters. AGDA+ achieves the optimal iteration complexity of $\\mathcal{O}(\\epsilon^{-2})$ and it is the first step-size search method for NCSC minimax problems that require only $3$ calls to $\\nabla f$ on average per backtracking iteration. The numerical experiments demonstrate its robustness and efficiency.","url_abs":"https://arxiv.org/abs/2406.14371v2","url_pdf":"https://arxiv.org/pdf/2406.14371v2.pdf","source":{"archive":"pwc-archive (Hugging Face), CC BY-SA 4.0","snapshot":"2025-07-28","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","row_kind":"links_only","authors_date_abstract":"arXiv metadata, CC0 1.0 (https://info.arxiv.org/help/license), from the Kaggle arXiv metadata snapshot of 2026-09-12"},"code_links":[{"paper_slug":"agda-proximal-alternating-gradient-descent","repo_url":"https://github.com/xuanzhangg/agda-plus","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":0,"framework":"pytorch","reach":null}],"tasks":[],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}