{"id":1160572,"date":"2026-01-20T10:06:44","date_gmt":"2026-01-20T18:06:44","guid":{"rendered":"https:\/\/www.microsoft.com\/en-us\/research\/?post_type=msr-research-item&p=1160572"},"modified":"2026-01-26T08:23:17","modified_gmt":"2026-01-26T16:23:17","slug":"distributed-policy-evaluation-under-multiple-behavior-strategies","status":"publish","type":"msr-research-item","link":"https:\/\/www.microsoft.com\/en-us\/research\/publication\/distributed-policy-evaluation-under-multiple-behavior-strategies\/","title":{"rendered":"Distributed Policy Evaluation Under Multiple Behavior Strategies"},"content":{"rendered":"

We apply diffusion strategies to develop a fully-distributed cooperative reinforcement learning algorithm in which agents in a network communicate only with their immediate neighbors to improve predictions about their environment. The algorithm can also be applied to off-policy learning, meaning that the agents can predict the response to a behavior different from the actual policies they are following. The proposed distributed strategy is efficient, with linear complexity in both computation time and memory footprint. We provide a mean-square-error performance analysis and establish convergence under constant step-size updates, which endow the network with continuous learning capabilities. The results show a clear gain from cooperation: when the individual agents can estimate the solution, cooperation increases stability and reduces bias and variance of the prediction error; but, more importantly, the network is able to approach the optimal solution even when none of the individual agents can (e.g., when the individual behavior policies restrict each agent to sample a small portion of the state space).<\/p>\n","protected":false},"excerpt":{"rendered":"

We apply diffusion strategies to develop a fully-distributed cooperative reinforcement learning algorithm in which agents in a network communicate only with their immediate neighbors to improve predictions about their environment. The algorithm can also be applied to off-policy learning, meaning that the agents can predict the response to a behavior different from the actual policies […]<\/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_organization":"","msr_pages_string":"","msr_page_range_start":"1260","msr_page_range_end":"1274","msr_series":"","msr_volume":"60","msr_copyright":"","msr_conference_name":"","msr_doi":"","msr_arxiv_id":"","msr_s2_paper_id":"","msr_mag_id":"","msr_pubmed_id":"","msr_other_authors":"","msr_other_contributors":"","msr_speaker":"","msr_award":"","msr_affiliation":"","msr_institution":"","msr_host":"","msr_version":"","msr_duration":"","msr_original_fields_of_study":null,"msr_release_tracker_id":"","msr_s2_match_type":"","msr_citation_count_updated":"","msr_published_date":"2013-12-29","msr_highlight_text":"","msr_notes":"","msr_longbiography":"","msr_publicationurl":"","msr_external_url":"","msr_secondary_video_url":"","msr_conference_url":"","msr_journal_url":"","msr_s2_pdf_url":"","msr_year":0,"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":null,"footnotes":""},"msr-research-highlight":[],"research-area":[13556],"msr-publication-type":[193715],"msr-publisher":[],"msr-focus-area":[],"msr-locale":[268875],"msr-post-option":[269148,269142],"msr-field-of-study":[246691],"msr-conference":[],"msr-journal":[270209],"msr-impact-theme":[],"msr-pillar":[],"class_list":["post-1160572","msr-research-item","type-msr-research-item","status-publish","hentry","msr-research-area-artificial-intelligence","msr-locale-en_us","msr-post-option-approved-for-river","msr-post-option-include-in-river","msr-field-of-study-computer-science"],"msr_publishername":"","msr_edition":"","msr_affiliation":"","msr_published_date":"2013-12-29","msr_host":"","msr_duration":"","msr_version":"","msr_speaker":"","msr_other_contributors":"","msr_booktitle":"","msr_pages_string":"","msr_chapter":"","msr_isbn":"","msr_journal":"","msr_volume":"60","msr_number":"","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":"","msr_publicationurl":"","msr_doi":"","msr_publication_uploader":[{"type":"doi","viewUrl":"false","id":"false","title":"https:\/\/doi.org\/10.1109\/TAC.2014.2368731","label_id":"243106","label":0},{"type":"url","viewUrl":"false","id":"false","title":"https:\/\/dblp.org\/rec\/journals\/corr\/MacuaCZS13.html","label_id":"243109","label":0},{"type":"url","viewUrl":"false","id":"false","title":"https:\/\/arxiv.org\/abs\/1312.7606","label_id":"243109","label":0},{"type":"url","viewUrl":"false","id":"false","title":"http:\/\/arxiv.org\/pdf\/1312.7606","label_id":"243109","label":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":[],"msr-author-ordering":[{"type":"text","value":"Sergio Valcarcel Macua","user_id":0,"rest_url":false},{"type":"text","value":"Jianshu Chen","user_id":0,"rest_url":false},{"type":"text","value":"S. 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