{"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/parallelizing-stochastic-gradient-descent-for","title":"Parallelizing Stochastic Gradient Descent for Least Squares Regression: mini-batching, averaging, and model misspecification","arxiv_id":"1610.03774","date":"2016-10-12","proceeding":null,"authors":["Prateek Jain","Sham M. Kakade","Rahul Kidambi","Praneeth Netrapalli","Aaron Sidford"],"abstract":"This work characterizes the benefits of averaging schemes widely used in\nconjunction with stochastic gradient descent (SGD). In particular, this work\nprovides a sharp analysis of: (1) mini-batching, a method of averaging many\nsamples of a stochastic gradient to both reduce the variance of the stochastic\ngradient estimate and for parallelizing SGD and (2) tail-averaging, a method\ninvolving averaging the final few iterates of SGD to decrease the variance in\nSGD's final iterate. This work presents non-asymptotic excess risk bounds for\nthese schemes for the stochastic approximation problem of least squares\nregression.\n  Furthermore, this work establishes a precise problem-dependent extent to\nwhich mini-batch SGD yields provable near-linear parallelization speedups over\nSGD with batch size one. This allows for understanding learning rate versus\nbatch size tradeoffs for the final iterate of an SGD method. These results are\nthen utilized in providing a highly parallelizable SGD method that obtains the\nminimax risk with nearly the same number of serial updates as batch gradient\ndescent, improving significantly over existing SGD methods. A non-asymptotic\nanalysis of communication efficient parallelization schemes such as\nmodel-averaging/parameter mixing methods is then provided.\n  Finally, this work sheds light on some fundamental differences in SGD's\nbehavior when dealing with agnostic noise in the (non-realizable) least squares\nregression problem. In particular, the work shows that the stepsizes that\nensure minimax risk for the agnostic case must be a function of the noise\nproperties.\n  This paper builds on the operator view of analyzing SGD methods, introduced\nby Defossez and Bach (2015), followed by developing a novel analysis in\nbounding these operators to characterize the excess risk. These techniques are\nof broader interest in analyzing computational aspects of stochastic\napproximation.","url_abs":"http://arxiv.org/abs/1610.03774v4","url_pdf":"http://arxiv.org/pdf/1610.03774v4.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":"parallelizing-stochastic-gradient-descent-for","repo_url":"https://github.com/rahulkidambi/AccSGD","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"pytorch","reach":{"status":"ok"}},{"paper_slug":"parallelizing-stochastic-gradient-descent-for","repo_url":"https://github.com/MindCode-4/code-11/tree/main/AccSGD-Parallelizing-Stochastic-Gradient-Descent","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":0,"framework":"mindspore","reach":{"status":"ok","spdx":"Apache-2.0"}},{"paper_slug":"parallelizing-stochastic-gradient-descent-for","repo_url":"https://github.com/MindCode-4/code-6/tree/main/AccSGD-Parallelizing-Stochastic-Gradient-Descent","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":0,"framework":"mindspore","reach":{"status":"ok","spdx":"Apache-2.0"}},{"paper_slug":"parallelizing-stochastic-gradient-descent-for","repo_url":"https://github.com/mindspore-ai/contrib/blob/master/application/AccSGD-Parallelizing-Stochastic-Gradient-Descent/AccSGD.py","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":0,"framework":"mindspore","reach":{"status":"ok","spdx":"Apache-2.0"}}],"tasks":[{"task_slug":"regression-1","task_name":"regression"}],"methods":[{"method_slug":"sgd","method_name":"SGD"}],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":"https://app.syntology.ai/?focus=1610.03774","mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}