{"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/finding-approximate-local-minima-faster-than","title":"Finding Approximate Local Minima Faster than Gradient Descent","arxiv_id":"1611.01146","date":"2016-11-03","proceeding":null,"authors":["Naman Agarwal","Zeyuan Allen-Zhu","Brian Bullins","Elad Hazan","Tengyu Ma"],"abstract":"We design a non-convex second-order optimization algorithm that is guaranteed\nto return an approximate local minimum in time which scales linearly in the\nunderlying dimension and the number of training examples. The time complexity\nof our algorithm to find an approximate local minimum is even faster than that\nof gradient descent to find a critical point. Our algorithm applies to a\ngeneral class of optimization problems including training a neural network and\nother non-convex objectives arising in machine learning.","url_abs":"http://arxiv.org/abs/1611.01146v4","url_pdf":"http://arxiv.org/pdf/1611.01146v4.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":"finding-approximate-local-minima-faster-than","repo_url":"https://github.com/vlad17/runlmc","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"none","reach":{"status":"unanswered"}}],"tasks":[{"task_slug":"machine-learning","task_name":"BIG-bench Machine Learning"}],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":"https://app.syntology.ai/?focus=1611.01146","mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}