Most contextual bandit algorithms minimize regret against the best fixed policy, a questionable benchmark for non-stationary environments that are ubiquitous in applications. In this work, we develop several efficient contextual bandit algorithms for non-stationary environments by equipping existing methods for i.i.d. problems with sophisticated statistical tests so as to dynamically adapt to a change in distribution.
\nWe analyze various standard notions of regret suited to non-stationary environments for these algorithms, including interval regret, switching regret, and dynamic regret. When competing with the best policy at each time, one of our algorithms achieves regret \\(O(\\sqrt{ST})\\) if there are \\(T\\) rounds with \\(S\\) stationary periods, or more generally \\(O(\\Delta^{1\/3}T^{2\/3})\\) where \\(\\Delta\\) is some non-stationarity measure. These results almost match the optimal guarantees achieved by an inefficient baseline that is a variant of the classic Exp4 algorithm. The dynamic regret result is also the first one for efficient and fully adversarial contextual bandit.
\nFurthermore, while the results above require tuning a parameter based on the unknown quantity \\(S\\) or \\(\\Delta\\), we also develop a parameter free algorithm achieving regret \\(\\min\\{S^{1\/4}T^{3\/4},\\Delta^{1\/5}T^{4\/5}\\}\\). This improves and generalizes the best existing result \\(\\Delta^{0.18}T^{0.82}\\) by Karnin and Anava (2016) which only holds for the two-armed bandit problem.<\/p>\n","protected":false},"excerpt":{"rendered":"
Most contextual bandit algorithms minimize regret against the best fixed policy, a questionable benchmark for non-stationary environments that are ubiquitous in applications. In this work, we develop several efficient contextual bandit algorithms for non-stationary environments by equipping existing methods for i.i.d. problems with sophisticated statistical tests so as to dynamically adapt to a change in […]<\/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":"","footnotes":""},"msr-content-type":[3],"msr-research-highlight":[],"research-area":[13556],"msr-publication-type":[193716],"msr-product-type":[],"msr-focus-area":[],"msr-platform":[],"msr-download-source":[],"msr-locale":[268875],"msr-post-option":[],"msr-field-of-study":[],"msr-conference":[],"msr-journal":[],"msr-impact-theme":[],"msr-pillar":[],"class_list":["post-489407","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":"2018-06-30","msr_host":"","msr_duration":"","msr_version":"","msr_speaker":"","msr_other_contributors":"","msr_booktitle":"Conference on Learning Theory","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":1,"msr_main_download":"","msr_publicationurl":"https:\/\/arxiv.org\/abs\/1708.01799","msr_doi":"","msr_publication_uploader":[{"type":"url","title":"https:\/\/arxiv.org\/abs\/1708.01799","viewUrl":false,"id":false,"label_id":0}],"msr_related_uploader":"","msr_attachments":[{"id":0,"url":"https:\/\/arxiv.org\/abs\/1708.01799"}],"msr-author-ordering":[{"type":"text","value":"Haipeng Luo","user_id":0,"rest_url":false},{"type":"text","value":"Chen-Yu Wei","user_id":0,"rest_url":false},{"type":"user_nicename","value":"Alekh Agarwal","user_id":30928,"rest_url":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/microsoft-research\/v1\/researchers?person=Alekh Agarwal"},{"type":"user_nicename","value":"John Langford","user_id":32204,"rest_url":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/microsoft-research\/v1\/researchers?person=John Langford"}],"msr_impact_theme":[],"msr_research_lab":[199571],"msr_event":[],"msr_group":[144902,395930],"msr_project":[568491],"publication":[],"video":[],"download":[],"msr_publication_type":"inproceedings","related_content":{"projects":[{"ID":568491,"post_title":"Real World Reinforcement Learning","post_name":"real-world-reinforcement-learning","post_type":"msr-project","post_date":"2019-05-03 10:02:09","post_modified":"2024-01-16 11:11:48","post_status":"publish","permalink":"https:\/\/www.microsoft.com\/en-us\/research\/project\/real-world-reinforcement-learning\/","post_excerpt":"The mission of Real World Reinforcement Learning (Real-World RL) team is to develop learning methods, from foundations to real world applications, to empower people and organizations to make better decisions. 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