{"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/on-graduated-optimization-for-stochastic-non","title":"On Graduated Optimization for Stochastic Non-Convex Problems","arxiv_id":"1503.03712","date":"2015-03-12","proceeding":null,"authors":["Elad Hazan","Kfir. Y. Levy","Shai Shalev-Shwartz"],"abstract":"The graduated optimization approach, also known as the continuation method,\nis a popular heuristic to solving non-convex problems that has received renewed\ninterest over the last decade. Despite its popularity, very little is known in\nterms of theoretical convergence analysis. In this paper we describe a new\nfirst-order algorithm based on graduated optimiza- tion and analyze its\nperformance. We characterize a parameterized family of non- convex functions\nfor which this algorithm provably converges to a global optimum. In particular,\nwe prove that the algorithm converges to an {\\epsilon}-approximate solution\nwithin O(1/\\epsilon^2) gradient-based steps. We extend our algorithm and\nanalysis to the setting of stochastic non-convex optimization with noisy\ngradient feedback, attaining the same convergence rate. Additionally, we\ndiscuss the setting of zero-order optimization, and devise a a variant of our\nalgorithm which converges at rate of O(d^2/\\epsilon^4).","url_abs":"http://arxiv.org/abs/1503.03712v2","url_pdf":"http://arxiv.org/pdf/1503.03712v2.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":"on-graduated-optimization-for-stochastic-non","repo_url":"https://github.com/ecotner/ConvexityAnnealing","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"tf","reach":{"status":"ok"}}],"tasks":[],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":"https://app.syntology.ai/?focus=1503.03712","mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}