{"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/decentralized-stochastic-optimization-and","title":"Decentralized Stochastic Optimization and Gossip Algorithms with Compressed Communication","arxiv_id":"1902.00340","date":"2019-02-01","proceeding":null,"authors":["Anastasia Koloskova","Sebastian U. Stich","Martin Jaggi"],"abstract":"We consider decentralized stochastic optimization with the objective function\n(e.g. data samples for machine learning task) being distributed over $n$\nmachines that can only communicate to their neighbors on a fixed communication\ngraph. To reduce the communication bottleneck, the nodes compress (e.g.\nquantize or sparsify) their model updates. We cover both unbiased and biased\ncompression operators with quality denoted by $\\omega \\leq 1$ ($\\omega=1$\nmeaning no compression). We (i) propose a novel gossip-based stochastic\ngradient descent algorithm, CHOCO-SGD, that converges at rate\n$\\mathcal{O}\\left(1/(nT) + 1/(T \\delta^2 \\omega)^2\\right)$ for strongly convex\nobjectives, where $T$ denotes the number of iterations and $\\delta$ the\neigengap of the connectivity matrix. Despite compression quality and network\nconnectivity affecting the higher order terms, the first term in the rate,\n$\\mathcal{O}(1/(nT))$, is the same as for the centralized baseline with exact\ncommunication. We (ii) present a novel gossip algorithm, CHOCO-GOSSIP, for the\naverage consensus problem that converges in time\n$\\mathcal{O}(1/(\\delta^2\\omega) \\log (1/\\epsilon))$ for accuracy $\\epsilon >\n0$. This is (up to our knowledge) the first gossip algorithm that supports\narbitrary compressed messages for $\\omega > 0$ and still exhibits linear\nconvergence. We (iii) show in experiments that both of our algorithms do\noutperform the respective state-of-the-art baselines and CHOCO-SGD can reduce\ncommunication by at least two orders of magnitudes.","url_abs":"http://arxiv.org/abs/1902.00340v1","url_pdf":"http://arxiv.org/pdf/1902.00340v1.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":"decentralized-stochastic-optimization-and","repo_url":"https://github.com/Adirlou/OptML_Project","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"none","reach":{"status":"ok"}},{"paper_slug":"decentralized-stochastic-optimization-and","repo_url":"https://github.com/JYWa/MATCHA","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"pytorch","reach":{"status":"ok"}},{"paper_slug":"decentralized-stochastic-optimization-and","repo_url":"https://github.com/epfml/ChocoSGD","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"pytorch","reach":{"status":"ok","spdx":"Apache-2.0"}}],"tasks":[{"task_slug":"stochastic-optimization","task_name":"Stochastic Optimization"}],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":"https://app.syntology.ai/?focus=1902.00340","mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}