{"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/gradient-methods-with-online-scaling","title":"Gradient Methods with Online Scaling","arxiv_id":"2411.01803","date":"2024-11-04","proceeding":null,"authors":["Wenzhi Gao","Ya-Chi Chu","Yinyu Ye","Madeleine Udell"],"abstract":"We introduce a framework to accelerate the convergence of gradient-based methods with online learning. The framework learns to scale the gradient at each iteration through an online learning algorithm and provably accelerates gradient-based methods asymptotically. In contrast with previous literature, where convergence is established based on worst-case analysis, our framework provides a strong convergence guarantee with respect to the optimal scaling matrix for the iteration trajectory. For smooth strongly convex optimization, our results provide an $O(\\kappa^\\star \\log(1/\\varepsilon)$) complexity result, where $\\kappa^\\star$ is the condition number achievable by the optimal preconditioner, improving on the previous $O(\\sqrt{n}\\kappa^\\star \\log(1/\\varepsilon))$ result. In particular, a variant of our method achieves superlinear convergence on convex quadratics. For smooth convex optimization, we show for the first time that the widely-used hypergradient descent heuristic improves on the convergence of gradient descent.","url_abs":"https://arxiv.org/abs/2411.01803v2","url_pdf":"https://arxiv.org/pdf/2411.01803v2.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":"gradient-methods-with-online-scaling","repo_url":"https://github.com/Gwzwpxz/osgm","is_official":1,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"none","reach":null}],"tasks":[],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}