{"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-tracking-for-high-dimensional","title":"Gradient Tracking for High Dimensional Federated Optimization","arxiv_id":"2312.05590","date":"2023-12-09","proceeding":null,"authors":["Jiadong Liang","Yang Peng","Zhihua Zhang"],"abstract":"In this paper, we study the (decentralized) distributed optimization problem with high-dimensional sparse structure. Building upon the FedDA algorithm, we propose a (Decentralized) FedDA-GT algorithm, which combines the \\textbf{gradient tracking} technique. It is able to eliminate the heterogeneity among different clients' objective functions while ensuring a dimension-free convergence rate. Compared to the vanilla FedDA approach, (D)FedDA-GT can significantly reduce the communication complexity, from ${O}(s^2\\log d/\\varepsilon^{3/2})$ to a more efficient ${O}(s^2\\log d/\\varepsilon)$. In cases where strong convexity is applicable, we introduce a multistep mechanism resulting in the Multistep ReFedDA-GT algorithm, a minor modified version of FedDA-GT. This approach achieves an impressive communication complexity of ${O}\\left(s\\log d \\log \\frac{1}{\\varepsilon}\\right)$ through repeated calls to the ReFedDA-GT algorithm. Finally, we conduct numerical experiments, illustrating that our proposed algorithms enjoy the dual advantage of being dimension-free and heterogeneity-free.","url_abs":"https://arxiv.org/abs/2312.05590v1","url_pdf":"https://arxiv.org/pdf/2312.05590v1.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":"gradient-tracking-for-high-dimensional","repo_url":"https://github.com/pengyang7881187/dfedda-gt","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":0,"framework":"jax","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}