{"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/sub-sampled-cubic-regularization-for-non","title":"Sub-sampled Cubic Regularization for Non-convex Optimization","arxiv_id":"1705.05933","date":"2017-05-16","proceeding":"ICML 2017 8","authors":["Jonas Moritz Kohler","Aurelien Lucchi"],"abstract":"We consider the minimization of non-convex functions that typically arise in\nmachine learning. Specifically, we focus our attention on a variant of trust\nregion methods known as cubic regularization. This approach is particularly\nattractive because it escapes strict saddle points and it provides stronger\nconvergence guarantees than first- and second-order as well as classical trust\nregion methods. However, it suffers from a high computational complexity that\nmakes it impractical for large-scale learning. Here, we propose a novel method\nthat uses sub-sampling to lower this computational cost. By the use of\nconcentration inequalities we provide a sampling scheme that gives sufficiently\naccurate gradient and Hessian approximations to retain the strong global and\nlocal convergence guarantees of cubically regularized methods. To the best of\nour knowledge this is the first work that gives global convergence guarantees\nfor a sub-sampled variant of cubic regularization on non-convex functions.\nFurthermore, we provide experimental results supporting our theory.","url_abs":"http://arxiv.org/abs/1705.05933v3","url_pdf":"http://arxiv.org/pdf/1705.05933v3.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":"sub-sampled-cubic-regularization-for-non","repo_url":"https://github.com/dalab/subsampled_cubic_regularization","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"none","reach":null},{"paper_slug":"sub-sampled-cubic-regularization-for-non","repo_url":"https://github.com/jonaskohler/subsampled_cubic_regularization","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"none","reach":null}],"tasks":[],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":"https://app.syntology.ai/?focus=1705.05933","mcp":{"get_harvested_code_for_paper":{"arxiv_id":"1705.05933"}},"developers":"https://syntology.ai/developers","read_at":"2026-09-24T18:15:14+00:00","read_at_is":"when the build read Syntology's graph, not when any sample ran","claim":"Per-sample execution status on synthesized fixtures; not a correctness claim about the paper. 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