{"id":607332,"date":"2019-09-05T11:02:20","date_gmt":"2019-09-05T18:02:20","guid":{"rendered":"https:\/\/www.microsoft.com\/en-us\/research\/?post_type=msr-research-item&#038;p=607332"},"modified":"2019-09-05T12:23:19","modified_gmt":"2019-09-05T19:23:19","slug":"model-selection-for-contextual-bandits","status":"publish","type":"msr-research-item","link":"https:\/\/www.microsoft.com\/en-us\/research\/publication\/model-selection-for-contextual-bandits\/","title":{"rendered":"Model selection for contextual bandits"},"content":{"rendered":"<p>We introduce the problem of model selection for contextual bandits, wherein a learner must adapt to the complexity of the optimal policy while balancing exploration and exploitation. Our main result is a new model selection guarantee for linear contextual bandits. We work in the stochastic realizable setting with a sequence of nested linear policy classes of dimension $d_1 < d_2 < \\ldots$\u00a0where the $<em>m^\\star$<\/em>-th class contains the optimal policy, and we design an algorithm that achieves $\\tilde{O}(T^{2\/3}d_{m^\\star}^{1\/3})$\u00a0regret with no prior knowledge of the optimal dimension $d_{m^\\star}$. The algorithm also achieves regret $\\tilde{O}(T^{3\/4} + \\sqrt{Td_{m^\\star}})$, which is optimal for $d_{m^\\star} \\geq \\sqrt{T}$. This is the first contextual bandit model selection result with non-vacuous regret for all values of $d_{m^\\star}$\u00a0and, to the best of our knowledge, is the first guarantee of its type in any contextual bandit setting. The core of the algorithm is a new estimator for the gap in best loss achievable by two linear policy classes, which we show admits a convergence rate faster than what is required to learn either class.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>We introduce the problem of model selection for contextual bandits, wherein a learner must adapt to the complexity of the optimal policy while balancing exploration and exploitation. Our main result is a new model selection guarantee for linear contextual bandits. We work in the stochastic realizable setting with a sequence of nested linear policy classes [&hellip;]<\/p>\n","protected":false},"featured_media":0,"template":"","meta":{"msr-url-field":"","msr-podcast-episode":"","msrModifiedDate":"","msrModifiedDateEnabled":false,"ep_exclude_from_search":false,"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-field-of-study":[],"msr-conference":[],"msr-journal":[],"msr-impact-theme":[],"msr-pillar":[],"class_list":["post-607332","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":"2019-12-1","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":1,"msr_main_download":"","msr_publicationurl":"","msr_doi":"","msr_publication_uploader":[{"type":"url","viewUrl":"false","id":"false","title":"https:\/\/arxiv.org\/abs\/1906.00531","label_id":"243109","label":0}],"msr_related_uploader":"","msr_attachments":[],"msr-author-ordering":[{"type":"guest","value":"dylan-foster","user_id":489920,"rest_url":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/microsoft-research\/v1\/researchers?person=dylan-foster"},{"type":"user_nicename","value":"Akshay 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