{"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/faster-stochastic-algorithms-for-minimax","title":"Faster Stochastic Algorithms for Minimax Optimization under Polyak--Łojasiewicz Conditions","arxiv_id":"2307.15868","date":"2023-07-29","proceeding":null,"authors":["Lesi Chen","Boyuan Yao","Luo Luo"],"abstract":"This paper considers stochastic first-order algorithms for minimax optimization under Polyak--{\\L}ojasiewicz (PL) conditions. We propose SPIDER-GDA for solving the finite-sum problem of the form $\\min_x \\max_y f(x,y)\\triangleq \\frac{1}{n} \\sum_{i=1}^n f_i(x,y)$, where the objective function $f(x,y)$ is $\\mu_x$-PL in $x$ and $\\mu_y$-PL in $y$; and each $f_i(x,y)$ is $L$-smooth. We prove SPIDER-GDA could find an $\\epsilon$-optimal solution within ${\\mathcal O}\\left((n + \\sqrt{n}\\,\\kappa_x\\kappa_y^2)\\log (1/\\epsilon)\\right)$ stochastic first-order oracle (SFO) complexity, which is better than the state-of-the-art method whose SFO upper bound is ${\\mathcal O}\\big((n + n^{2/3}\\kappa_x\\kappa_y^2)\\log (1/\\epsilon)\\big)$, where $\\kappa_x\\triangleq L/\\mu_x$ and $\\kappa_y\\triangleq L/\\mu_y$. For the ill-conditioned case, we provide an accelerated algorithm to reduce the computational cost further. It achieves $\\tilde{{\\mathcal O}}\\big((n+\\sqrt{n}\\,\\kappa_x\\kappa_y)\\log^2 (1/\\epsilon)\\big)$ SFO upper bound when $\\kappa_y \\gtrsim \\sqrt{n}$. Our ideas also can be applied to the more general setting that the objective function only satisfies PL condition for one variable. Numerical experiments validate the superiority of proposed methods.","url_abs":"https://arxiv.org/abs/2307.15868v1","url_pdf":"https://arxiv.org/pdf/2307.15868v1.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":"abstracts"},"code_links":[{"paper_slug":"faster-stochastic-algorithms-for-minimax","repo_url":"https://github.com/truenobility303/spider-gda","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":0,"framework":"none","reach":{"status":"ok"}}],"tasks":[],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":"https://app.syntology.ai/?focus=2307.15868","mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}