{"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/the-nesterov-spokoiny-acceleration-o-1-k-2","title":"The Nesterov-Spokoiny Acceleration Achieves Strict $o(1/k^2)$ Convergence","arxiv_id":"2308.14314","date":"2023-08-28","proceeding":null,"authors":["Weibin Peng","Yu Liu","Tianyu Wang"],"abstract":"This paper studies the Nesterov-Spokoiny Acceleration (NSA), a variant of the accelerated gradient method by Nesterov and Spokoiny. For smooth convex optimization, NSA achieves a strict $o(1/k^2)$ convergence rate in function value and an $o(1/(k^3 \\log k))$ rate in squared gradient norm, while ensuring monotonic descent of the objective. We further study a zeroth-order version of NSA that handles inexact gradients, and extends NSA to composite optimization problems, in each case establishing $o(1/k^2)$ convergence in function value. A continuous-time analysis reveals connections to high-resolution ODEs known to underlie acceleration phenomena.","url_abs":"https://arxiv.org/abs/2308.14314v4","url_pdf":"https://arxiv.org/pdf/2308.14314v4.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":"the-nesterov-spokoiny-acceleration-o-1-k-2","repo_url":"https://github.com/bumsu-kim/cars","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":0,"framework":"none","reach":null}],"tasks":[],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"syntology_url":null,"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}