{"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/complexity-guarantees-for-polyak-steps-with","title":"Complexity Guarantees for Polyak Steps with Momentum","arxiv_id":"2002.00915","date":"2020-02-03","proceeding":null,"authors":["Mathieu Barré","Adrien Taylor","Alexandre d'Aspremont"],"abstract":"In smooth strongly convex optimization, knowledge of the strong convexity parameter is critical for obtaining simple methods with accelerated rates. In this work, we study a class of methods, based on Polyak steps, where this knowledge is substituted by that of the optimal value, $f_*$. We first show slightly improved convergence bounds than previously known for the classical case of simple gradient descent with Polyak steps, we then derive an accelerated gradient method with Polyak steps and momentum, along with convergence guarantees.","url_abs":"https://arxiv.org/abs/2002.00915v2","url_pdf":"https://arxiv.org/pdf/2002.00915v2.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":"complexity-guarantees-for-polyak-steps-with","repo_url":"https://github.com/mathbarre/PerformanceEstimationPolyakSteps","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":1,"framework":"none","reach":{"status":"ok"}}],"tasks":[],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":"https://app.syntology.ai/?focus=2002.00915","mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}