{"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/stochastic-subgradient-method-converges-at","title":"Stochastic subgradient method converges at the rate $O(k^{-1/4})$ on weakly convex functions","arxiv_id":"1802.02988","date":"2018-02-08","proceeding":null,"authors":["Damek Davis","Dmitriy Drusvyatskiy"],"abstract":"We prove that the proximal stochastic subgradient method, applied to a weakly\nconvex problem, drives the gradient of the Moreau envelope to zero at the rate\n$O(k^{-1/4})$. As a consequence, we resolve an open question on the convergence\nrate of the proximal stochastic gradient method for minimizing the sum of a\nsmooth nonconvex function and a convex proximable function.","url_abs":"http://arxiv.org/abs/1802.02988v3","url_pdf":"http://arxiv.org/pdf/1802.02988v3.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":"stochastic-subgradient-method-converges-at","repo_url":"https://github.com/POLane16/DIAG","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"none","reach":{"status":"ok"}},{"paper_slug":"stochastic-subgradient-method-converges-at","repo_url":"https://github.com/tkkiran/DIAG","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"none","reach":null}],"tasks":[{"task_slug":"open-question","task_name":"Open-Ended Question Answering"}],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"syntology_url":null,"atlas_url":"https://app.syntology.ai/?focus=1802.02988","mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}