{"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/non-convex-finite-sum-optimization-via-scsg-1","title":"Non-convex Finite-Sum Optimization Via SCSG Methods","arxiv_id":"1706.09156","date":"2017-06-28","proceeding":null,"authors":["Lihua Lei","Cheng Ju","Jianbo Chen","Michael I. Jordan"],"abstract":"We develop a class of algorithms, as variants of the stochastically controlled stochastic gradient (SCSG) methods (Lei and Jordan, 2016), for the smooth non-convex finite-sum optimization problem. Assuming the smoothness of each component, the complexity of SCSG to reach a stationary point with $\\mathbb{E} \\|\\nabla f(x)\\|^{2}\\le \\epsilon$ is $O\\left (\\min\\{\\epsilon^{-5/3}, \\epsilon^{-1}n^{2/3}\\}\\right)$, which strictly outperforms the stochastic gradient descent. Moreover, SCSG is never worse than the state-of-the-art methods based on variance reduction and it significantly outperforms them when the target accuracy is low. A similar acceleration is also achieved when the functions satisfy the Polyak-Lojasiewicz condition. Empirical experiments demonstrate that SCSG outperforms stochastic gradient methods on training multi-layers neural networks in terms of both training and validation loss.","url_abs":"http://arxiv.org/abs/1706.09156v4","url_pdf":"http://arxiv.org/pdf/1706.09156v4.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":"links_only","authors_date_abstract":"arXiv metadata, CC0 1.0 (https://info.arxiv.org/help/license), from the Kaggle arXiv metadata snapshot of 2026-09-12"},"code_links":[{"paper_slug":"non-convex-finite-sum-optimization-via-scsg-1","repo_url":"https://github.com/Jianbo-Lab/SCSG","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":0,"framework":"tf","reach":{"status":"unanswered"}},{"paper_slug":"non-convex-finite-sum-optimization-via-scsg-1","repo_url":"https://github.com/SamuelHorvath/Variance_Reduced_Optimizers_Pytorch","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"pytorch","reach":{"status":"ok","spdx":"Apache-2.0"}}],"tasks":[],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"syntology_url":"https://syntology.ai/paper/1706.09156","atlas_url":"https://app.syntology.ai/?focus=1706.09156","mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}