{"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/arock-an-algorithmic-framework-for","title":"ARock: an Algorithmic Framework for Asynchronous Parallel Coordinate Updates","arxiv_id":"1506.02396","date":"2015-06-08","proceeding":null,"authors":["Zhimin Peng","Yangyang Xu","Ming Yan","Wotao Yin"],"abstract":"Finding a fixed point to a nonexpansive operator, i.e., $x^*=Tx^*$, abstracts\nmany problems in numerical linear algebra, optimization, and other areas of\nscientific computing. To solve fixed-point problems, we propose ARock, an\nalgorithmic framework in which multiple agents (machines, processors, or cores)\nupdate $x$ in an asynchronous parallel fashion. Asynchrony is crucial to\nparallel computing since it reduces synchronization wait, relaxes communication\nbottleneck, and thus speeds up computing significantly. At each step of ARock,\nan agent updates a randomly selected coordinate $x_i$ based on possibly\nout-of-date information on $x$. The agents share $x$ through either global\nmemory or communication. If writing $x_i$ is atomic, the agents can read and\nwrite $x$ without memory locks.\n  Theoretically, we show that if the nonexpansive operator $T$ has a fixed\npoint, then with probability one, ARock generates a sequence that converges to\na fixed points of $T$. Our conditions on $T$ and step sizes are weaker than\ncomparable work. Linear convergence is also obtained.\n  We propose special cases of ARock for linear systems, convex optimization,\nmachine learning, as well as distributed and decentralized consensus problems.\nNumerical experiments of solving sparse logistic regression problems are\npresented.","url_abs":"http://arxiv.org/abs/1506.02396v5","url_pdf":"http://arxiv.org/pdf/1506.02396v5.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":"arock-an-algorithmic-framework-for","repo_url":"https://github.com/uclaopt/TMAC","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"none","reach":{"status":"ok"}}],"tasks":[],"methods":[{"method_slug":"logistic-regression","method_name":"Logistic Regression"}],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":"https://app.syntology.ai/?focus=1506.02396","mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}