{"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/on-curvature-aided-incremental-aggregated","title":"Accelerating Incremental Gradient Optimization with Curvature Information","arxiv_id":"1806.00125","date":"2018-05-31","proceeding":null,"authors":["Hoi-To Wai","Wei Shi","Cesar A. Uribe","Angelia Nedich","Anna Scaglione"],"abstract":"This paper studies an acceleration technique for incremental aggregated gradient ({\\sf IAG}) method through the use of \\emph{curvature} information for solving strongly convex finite sum optimization problems. These optimization problems of interest arise in large-scale learning applications. Our technique utilizes a curvature-aided gradient tracking step to produce accurate gradient estimates incrementally using Hessian information. We propose and analyze two methods utilizing the new technique, the curvature-aided IAG ({\\sf CIAG}) method and the accelerated CIAG ({\\sf A-CIAG}) method, which are analogous to gradient method and Nesterov's accelerated gradient method, respectively. Setting $\\kappa$ to be the condition number of the objective function, we prove the $R$ linear convergence rates of $1 - \\frac{4c_0 \\kappa}{(\\kappa+1)^2}$ for the {\\sf CIAG} method, and $1 - \\sqrt{\\frac{c_1}{2\\kappa}}$ for the {\\sf A-CIAG} method, where $c_0,c_1 \\leq 1$ are constants inversely proportional to the distance between the initial point and the optimal solution. When the initial iterate is close to the optimal solution, the $R$ linear convergence rates match with the gradient and accelerated gradient method, albeit {\\sf CIAG} and {\\sf A-CIAG} operate in an incremental setting with strictly lower computation complexity. Numerical experiments confirm our findings. The source codes used for this paper can be found on \\url{http://github.com/hoitowai/ciag/}.","url_abs":"https://arxiv.org/abs/1806.00125v2","url_pdf":"https://arxiv.org/pdf/1806.00125v2.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":"on-curvature-aided-incremental-aggregated","repo_url":"https://github.com/hoitowai/ciag","is_official":1,"mentioned_in_paper":1,"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}