{"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/s-addopt-decentralized-stochastic-first-order","title":"S-ADDOPT: Decentralized stochastic first-order optimization over directed graphs","arxiv_id":"2005.07785","date":"2020-05-15","proceeding":null,"authors":["Muhammad I. Qureshi","Ran Xin","Soummya Kar","Usman A. Khan"],"abstract":"In this report, we study decentralized stochastic optimization to minimize a sum of smooth and strongly convex cost functions when the functions are distributed over a directed network of nodes. In contrast to the existing work, we use gradient tracking to improve certain aspects of the resulting algorithm. In particular, we propose the~\\textbf{\\texttt{S-ADDOPT}} algorithm that assumes a stochastic first-order oracle at each node and show that for a constant step-size~$\\alpha$, each node converges linearly inside an error ball around the optimal solution, the size of which is controlled by~$\\alpha$. For decaying step-sizes~$\\mathcal{O}(1/k)$, we show that~\\textbf{\\texttt{S-ADDOPT}} reaches the exact solution sublinearly at~$\\mathcal{O}(1/k)$ and its convergence is asymptotically network-independent. Thus the asymptotic behavior of~\\textbf{\\texttt{S-ADDOPT}} is comparable to the centralized stochastic gradient descent. Numerical experiments over both strongly convex and non-convex problems illustrate the convergence behavior and the performance comparison of the proposed algorithm.","url_abs":"https://arxiv.org/abs/2005.07785v3","url_pdf":"https://arxiv.org/pdf/2005.07785v3.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":"s-addopt-decentralized-stochastic-first-order","repo_url":"https://github.com/qureshi-mi/S-ADDOPT","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"tf","reach":null},{"paper_slug":"s-addopt-decentralized-stochastic-first-order","repo_url":"https://github.com/qureshi-mi/SADDOPT","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"tf","reach":null}],"tasks":[{"task_slug":"stochastic-optimization","task_name":"Stochastic Optimization"}],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}