{"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-on","title":"Stochastic subgradient method converges on tame functions","arxiv_id":"1804.07795","date":"2018-04-20","proceeding":null,"authors":["Damek Davis","Dmitriy Drusvyatskiy","Sham Kakade","Jason D. Lee"],"abstract":"This work considers the question: what convergence guarantees does the\nstochastic subgradient method have in the absence of smoothness and convexity?\nWe prove that the stochastic subgradient method, on any semialgebraic locally\nLipschitz function, produces limit points that are all first-order stationary.\nMore generally, our result applies to any function with a Whitney stratifiable\ngraph. In particular, this work endows the stochastic subgradient method, and\nits proximal extension, with rigorous convergence guarantees for a wide class\nof problems arising in data science---including all popular deep learning\narchitectures.","url_abs":"http://arxiv.org/abs/1804.07795v3","url_pdf":"http://arxiv.org/pdf/1804.07795v3.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-on","repo_url":"https://github.com/IBM/FormalML","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"none","reach":{"status":"ok","spdx":"Apache-2.0"}}],"tasks":[],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":"https://app.syntology.ai/?focus=1804.07795","mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}