{"id":884556,"date":"2022-10-10T20:59:32","date_gmt":"2022-10-11T03:59:32","guid":{"rendered":"https:\/\/www.microsoft.com\/en-us\/research\/"},"modified":"2022-10-10T20:59:32","modified_gmt":"2022-10-11T03:59:32","slug":"restless-ucb-an-efficient-and-low-complexity-algorithm-for-online-restless-bandits","status":"publish","type":"msr-research-item","link":"https:\/\/www.microsoft.com\/en-us\/research\/publication\/restless-ucb-an-efficient-and-low-complexity-algorithm-for-online-restless-bandits\/","title":{"rendered":"Restless-UCB, an Efficient and Low-complexity Algorithm for Online Restless Bandits"},"content":{"rendered":"<p>We study the online restless bandit problem, where the state of each arm evolves according to a Markov chain, and the reward of pulling an arm depends on both the pulled arm and the current state of the corresponding Markov chain. In this paper, we propose Restless-UCB, a learning policy that follows the explore-then-commit framework. In Restless-UCB, we present a novel method to construct offline instances, which only requires <span style=\"color: #212529;font-family: -apple-system, BlinkMacSystemFont, Segoe UI, Roboto, Helvetica Neue, Arial, Noto Sans, sans-serif, Apple Color Emoji, Segoe UI Emoji, Segoe UI Symbol, Noto Color Emoji\"><span style=\"font-size: 18.08px\">$O(N)$<\/span><\/span> time-complexity ($N$ is the number of arms) and is exponentially better than the complexity of existing learning policy. We also prove that Restless-UCB achieves a regret upper bound of $\\tilde{O}((N+M^3)T^{2\\over 3})$, where <span style=\"color: #212529;font-family: -apple-system, BlinkMacSystemFont, Segoe UI, Roboto, Helvetica Neue, Arial, Noto Sans, sans-serif, Apple Color Emoji, Segoe UI Emoji, Segoe UI Symbol, Noto Color Emoji\"><span style=\"font-size: 18.08px\">$M$<\/span><\/span> is the Markov chain state space size and $T$ is the time horizon. Compared to existing algorithms, our result eliminates the exponential factor (in <span style=\"color: #212529;font-family: -apple-system, BlinkMacSystemFont, Segoe UI, Roboto, Helvetica Neue, Arial, Noto Sans, sans-serif, Apple Color Emoji, Segoe UI Emoji, Segoe UI Symbol, Noto Color Emoji\"><span style=\"font-size: 18.08px\">$M,N$<\/span><\/span>) in the regret upper bound, due to a novel exploitation of the sparsity in transitions in general restless bandit problems. As a result, our analysis technique can also be adopted to tighten the regret bounds of existing algorithms. Finally, we conduct experiments based on real-world dataset, to compare the Restless-UCB policy with state-of-the-art benchmarks. Our results show that Restless-UCB outperforms existing algorithms in regret, and significantly reduces the running time.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>We study the online restless bandit problem, where the state of each arm evolves according to a Markov chain, and the reward of pulling an arm depends on both the pulled arm and the current state of the corresponding Markov chain. In this paper, we propose Restless-UCB, a learning policy that follows the explore-then-commit framework. [&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_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":"","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":"2020-12-12","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":false,"msr_s2_open_access":false,"msr_s2_author_ids":[],"msr_pub_ids":[],"msr_hide_image_in_river":0,"footnotes":""},"msr-research-highlight":[],"research-area":[13556],"msr-publication-type":[193716],"msr-publisher":[],"msr-focus-area":[],"msr-locale":[268875],"msr-post-option":[],"msr-field-of-study":[],"msr-conference":[259048],"msr-journal":[],"msr-impact-theme":[],"msr-pillar":[],"class_list":["post-884556","msr-research-item","type-msr-research-item","status-publish","hentry","msr-research-area-artificial-intelligence","msr-locale-en_us"],"msr_publishername":"","msr_edition":"","msr_affiliation":"","msr_published_date":"2020-12-12","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_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":0,"msr_main_download":"","msr_publicationurl":"","msr_doi":"","msr_publication_uploader":[{"type":"url","viewUrl":"false","id":"false","title":"https:\/\/arxiv.org\/pdf\/2011.02664.pdf","label_id":"243132","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":"user_nicename","value":"Siwei Wang","user_id":42321,"rest_url":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/microsoft-research\/v1\/researchers?person=Siwei Wang"},{"type":"text","value":"Longbo Huang","user_id":0,"rest_url":false},{"type":"text","value":"John C.S. 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