{"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/momentum-based-variance-reduction-in-non","title":"Momentum-Based Variance Reduction in Non-Convex SGD","arxiv_id":"1905.10018","date":"2019-05-24","proceeding":"NeurIPS 2019 12","authors":["Ashok Cutkosky","Francesco Orabona"],"abstract":"Variance reduction has emerged in recent years as a strong competitor to stochastic gradient descent in non-convex problems, providing the first algorithms to improve upon the converge rate of stochastic gradient descent for finding first-order critical points. However, variance reduction techniques typically require carefully tuned learning rates and willingness to use excessively large \"mega-batches\" in order to achieve their improved results. We present a new algorithm, STORM, that does not require any batches and makes use of adaptive learning rates, enabling simpler implementation and less hyperparameter tuning. Our technique for removing the batches uses a variant of momentum to achieve variance reduction in non-convex optimization. On smooth losses $F$, STORM finds a point $\\boldsymbol{x}$ with $\\mathbb{E}[\\|\\nabla F(\\boldsymbol{x})\\|]\\le O(1/\\sqrt{T}+\\sigma^{1/3}/T^{1/3})$ in $T$ iterations with $\\sigma^2$ variance in the gradients, matching the optimal rate but without requiring knowledge of $\\sigma$.","url_abs":"https://arxiv.org/abs/1905.10018v3","url_pdf":"https://arxiv.org/pdf/1905.10018v3.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":"momentum-based-variance-reduction-in-non","repo_url":"https://github.com/google-research/google-research","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":0,"framework":"tf","reach":null},{"paper_slug":"momentum-based-variance-reduction-in-non","repo_url":"https://github.com/duanzhiihao/PyTorch_OLoptim","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"pytorch","reach":{"status":"ok"}}],"tasks":[],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":"https://app.syntology.ai/?focus=1905.10018","mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}