{"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/optimal-algorithms-for-smooth-and-strongly","title":"Optimal algorithms for smooth and strongly convex distributed optimization in networks","arxiv_id":"1702.08704","date":"2017-02-28","proceeding":"ICML 2017 8","authors":["Kevin Scaman","Francis Bach","Sébastien Bubeck","Yin Tat Lee","Laurent Massoulié"],"abstract":"In this paper, we determine the optimal convergence rates for strongly convex\nand smooth distributed optimization in two settings: centralized and\ndecentralized communications over a network. For centralized (i.e.\nmaster/slave) algorithms, we show that distributing Nesterov's accelerated\ngradient descent is optimal and achieves a precision $\\varepsilon > 0$ in time\n$O(\\sqrt{\\kappa_g}(1+\\Delta\\tau)\\ln(1/\\varepsilon))$, where $\\kappa_g$ is the\ncondition number of the (global) function to optimize, $\\Delta$ is the diameter\nof the network, and $\\tau$ (resp. $1$) is the time needed to communicate values\nbetween two neighbors (resp. perform local computations). For decentralized\nalgorithms based on gossip, we provide the first optimal algorithm, called the\nmulti-step dual accelerated (MSDA) method, that achieves a precision\n$\\varepsilon > 0$ in time\n$O(\\sqrt{\\kappa_l}(1+\\frac{\\tau}{\\sqrt{\\gamma}})\\ln(1/\\varepsilon))$, where\n$\\kappa_l$ is the condition number of the local functions and $\\gamma$ is the\n(normalized) eigengap of the gossip matrix used for communication between\nnodes. We then verify the efficiency of MSDA against state-of-the-art methods\nfor two problems: least-squares regression and classification by logistic\nregression.","url_abs":"http://arxiv.org/abs/1702.08704v2","url_pdf":"http://arxiv.org/pdf/1702.08704v2.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":"optimal-algorithms-for-smooth-and-strongly","repo_url":"https://github.com/adelnabli/dadao","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"pytorch","reach":{"status":"ok"}}],"tasks":[{"task_slug":"distributed-optimization","task_name":"Distributed Optimization"},{"task_slug":"regression-1","task_name":"regression"}],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":"https://app.syntology.ai/?focus=1702.08704","mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}