{"id":167868,"date":"2015-01-01T00:00:00","date_gmt":"2015-01-01T00:00:00","guid":{"rendered":"https:\/\/www.microsoft.com\/en-us\/research\/msr-research-item\/communication-efficient-distributed-optimization-of-self-concordant-empirical-loss-2\/"},"modified":"2018-10-16T21:29:52","modified_gmt":"2018-10-17T04:29:52","slug":"communication-efficient-distributed-optimization-of-self-concordant-empirical-loss-2","status":"publish","type":"msr-research-item","link":"https:\/\/www.microsoft.com\/en-us\/research\/publication\/communication-efficient-distributed-optimization-of-self-concordant-empirical-loss-2\/","title":{"rendered":"Communication-Efficient Distributed Optimization of Self-Concordant Empirical Loss"},"content":{"rendered":"<div class=\"asset-content\">\n<p>We consider distributed convex optimization problems originated from sample average approximation of stochastic optimization, or empirical risk minimization in machine learning. We assume that each machine in the distributed computing system has access to a local empirical loss function, constructed with i.i.d. data sampled from a common distribution. We propose a communication-efficient distributed algorithm to minimize the overall empirical loss, which is the average of the local empirical losses. The algorithm is based on an inexact damped Newton method, where the inexact Newton steps are computed by a distributed preconditioned conjugate gradient method. We analyze its iteration complexity and communication efficiency for minimizing self-concordant empirical loss functions, and discuss the results for distributed ridge regression, logistic regression and binary classification with a smoothed hinge loss. In a standard setting for supervised learning, the required number of communication rounds of the algorithm does not increase with the sample size, and only grows slowly with the number of machines.<\/p>\n<\/div>\n<p><!-- .asset-content --><\/p>\n","protected":false},"excerpt":{"rendered":"<p>We consider distributed convex optimization problems originated from sample average approximation of stochastic optimization, or empirical risk minimization in machine learning. We assume that each machine in the distributed computing system has access to a local empirical loss function, constructed with i.i.d. data sampled from a common distribution. We propose a communication-efficient distributed algorithm to [&hellip;]<\/p>\n","protected":false},"featured_media":0,"template":"","meta":{"msr-url-field":"","msr-podcast-episode":"","msrModifiedDate":"","msrModifiedDateEnabled":false,"ep_exclude_from_search":false,"_classifai_error":"","msr-author-ordering":null,"msr_publishername":"","msr_publisher_other":"","msr_booktitle":"","msr_chapter":"","msr_edition":"","msr_editors":"","msr_how_published":"","msr_isbn":"","msr_issue":"","msr_journal":"","msr_number":"MSR-TR-2015-1","msr_organization":"","msr_pages_string":"","msr_page_range_start":"","msr_page_range_end":"","msr_series":"","msr_volume":"","msr_copyright":"","msr_conference_name":"","msr_doi":"","msr_arxiv_id":"","msr_s2_paper_id":"","msr_mag_id":"","msr_pubmed_id":"","msr_other_authors":"Yuchen Zhang","msr_other_contributors":"","msr_speaker":"","msr_award":"","msr_affiliation":"","msr_institution":"","msr_host":"","msr_version":"","msr_duration":"","msr_original_fields_of_study":"","msr_release_tracker_id":"","msr_s2_match_type":"","msr_citation_count_updated":"","msr_published_date":"2015-01-01","msr_highlight_text":"","msr_notes":"","msr_longbiography":"","msr_publicationurl":"https:\/\/arxiv.org\/abs\/1501.00263","msr_external_url":"","msr_secondary_video_url":"","msr_conference_url":"","msr_journal_url":"","msr_s2_pdf_url":"","msr_year":2015,"msr_citation_count":0,"msr_influential_citations":0,"msr_reference_count":0,"msr_s2_match_confidence":0,"msr_microsoftintellectualproperty":true,"msr_s2_open_access":false,"msr_s2_author_ids":[],"msr_pub_ids":[],"msr_hide_image_in_river":0,"footnotes":""},"msr-research-highlight":[],"research-area":[13561,13556],"msr-publication-type":[193718],"msr-publisher":[],"msr-focus-area":[],"msr-locale":[268875],"msr-post-option":[],"msr-field-of-study":[],"msr-conference":[],"msr-journal":[],"msr-impact-theme":[],"msr-pillar":[],"class_list":["post-167868","msr-research-item","type-msr-research-item","status-publish","hentry","msr-research-area-algorithms","msr-research-area-artificial-intelligence","msr-locale-en_us"],"msr_publishername":"","msr_edition":"","msr_affiliation":"","msr_published_date":"2015-01-01","msr_host":"","msr_duration":"","msr_version":"","msr_speaker":"","msr_other_contributors":"","msr_booktitle":"","msr_pages_string":"","msr_chapter":"","msr_isbn":"","msr_journal":"","msr_volume":"","msr_number":"MSR-TR-2015-1","msr_editors":"","msr_series":"","msr_issue":"","msr_organization":"","msr_how_published":"","msr_notes":"","msr_highlight_text":"","msr_release_tracker_id":"","msr_original_fields_of_study":"","msr_download_urls":"","msr_external_url":"","msr_secondary_video_url":"","msr_longbiography":"","msr_microsoftintellectualproperty":1,"msr_main_download":"204530","msr_publicationurl":"https:\/\/arxiv.org\/abs\/1501.00263","msr_doi":"","msr_publication_uploader":[{"type":"file","title":"DiSCO_paper.pdf","viewUrl":"https:\/\/www.microsoft.com\/en-us\/research\/wp-content\/uploads\/2016\/02\/DiSCO_paper.pdf","id":204530,"label_id":0},{"type":"url","title":"https:\/\/arxiv.org\/abs\/1501.00263","viewUrl":false,"id":false,"label_id":0}],"msr_related_uploader":"","msr_citation_count":0,"msr_citation_count_updated":"","msr_s2_paper_id":"","msr_influential_citations":0,"msr_reference_count":0,"msr_arxiv_id":"","msr_s2_author_ids":[],"msr_s2_open_access":false,"msr_s2_pdf_url":null,"msr_attachments":[{"id":0,"url":"https:\/\/arxiv.org\/abs\/1501.00263"},{"id":204530,"url":"https:\/\/www.microsoft.com\/en-us\/research\/wp-content\/uploads\/2016\/02\/DiSCO_paper.pdf"}],"msr-author-ordering":[{"type":"text","value":"Yuchen Zhang","user_id":0,"rest_url":false},{"type":"user_nicename","value":"lixiao","user_id":32713,"rest_url":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/microsoft-research\/v1\/researchers?person=lixiao"}],"msr_impact_theme":[],"msr_research_lab":[199565],"msr_event":[],"msr_group":[],"msr_project":[392777],"publication":[],"video":[],"msr-tool":[],"msr_publication_type":"techreport","related_content":{"projects":[{"ID":392777,"post_title":"Foundations of Optimization","post_name":"foundations-of-optimization","post_type":"msr-project","post_date":"2017-07-06 09:30:53","post_modified":"2018-12-04 14:12:39","post_status":"publish","permalink":"https:\/\/www.microsoft.com\/en-us\/research\/project\/foundations-of-optimization\/","post_excerpt":"Optimization methods are the engine of machine learning algorithms. Examples abound, such as training neural networks with stochastic gradient descent, segmenting images with submodular optimization, or efficiently searching a game tree with bandit algorithms. We aim to advance the mathematical foundations of both discrete and continuous optimization and to leverage these advances to develop new algorithms with a broad set of AI applications. 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