{"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/parallel-coordinate-descent-newton-method-for","title":"Parallel Coordinate Descent Newton Method for Efficient $\\ell_1$-Regularized Minimization","arxiv_id":"1306.4080","date":"2013-06-18","proceeding":null,"authors":["An Bian","Xiong Li","Yuncai Liu","Ming-Hsuan Yang"],"abstract":"The recent years have witnessed advances in parallel algorithms for large\nscale optimization problems. Notwithstanding demonstrated success, existing\nalgorithms that parallelize over features are usually limited by divergence\nissues under high parallelism or require data preprocessing to alleviate these\nproblems. In this work, we propose a Parallel Coordinate Descent Newton\nalgorithm using multidimensional approximate Newton steps (PCDN), where the\noff-diagonal elements of the Hessian are set to zero to enable parallelization.\nIt randomly partitions the feature set into $b$ bundles/subsets with size of\n$P$, and sequentially processes each bundle by first computing the descent\ndirections for each feature in parallel and then conducting $P$-dimensional\nline search to obtain the step size. We show that: (1) PCDN is guaranteed to\nconverge globally despite increasing parallelism; (2) PCDN converges to the\nspecified accuracy $\\epsilon$ within the limited iteration number of\n$T_\\epsilon$, and $T_\\epsilon$ decreases with increasing parallelism (bundle\nsize $P$). Using the implementation technique of maintaining intermediate\nquantities, we minimize the data transfer and synchronization cost of the\n$P$-dimensional line search. For concreteness, the proposed PCDN algorithm is\napplied to $\\ell_1$-regularized logistic regression and $\\ell_2$-loss SVM.\nExperimental evaluations on six benchmark datasets show that the proposed PCDN\nalgorithm exploits parallelism well and outperforms the state-of-the-art\nmethods in speed without losing accuracy.","url_abs":"http://arxiv.org/abs/1306.4080v4","url_pdf":"http://arxiv.org/pdf/1306.4080v4.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":"parallel-coordinate-descent-newton-method-for","repo_url":"https://github.com/bianan/ParallelCDN","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":1,"framework":"none","reach":null}],"tasks":[],"methods":[{"method_slug":"logistic-regression","method_name":"Logistic Regression"},{"method_slug":"speed","method_name":"SPEED"},{"method_slug":"svm","method_name":"SVM"}],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}