{"id":167936,"date":"2015-05-01T00:00:00","date_gmt":"2015-05-01T00:00:00","guid":{"rendered":"https:\/\/www.microsoft.com\/en-us\/research\/msr-research-item\/toward-minimax-off-policy-value-estimation\/"},"modified":"2018-10-16T20:02:10","modified_gmt":"2018-10-17T03:02:10","slug":"toward-minimax-off-policy-value-estimation","status":"publish","type":"msr-research-item","link":"https:\/\/www.microsoft.com\/en-us\/research\/publication\/toward-minimax-off-policy-value-estimation\/","title":{"rendered":"Toward Minimax Off-policy Value Estimation"},"content":{"rendered":"<div class=\"asset-content\">\n<p>This paper studies the off-policy evaluation problem, where one aims to estimate the value of a target policy based on a sample of observations collected by another policy. We first consider the single-state, or multi-armed bandit case, establish a finite-time minimax risk lower bound, and analyze the risk of three standard estimators. For the so-called regression estimator, we show that while it is asymptotically optimal, for small sample sizes it may perform suboptimally compared to an ideal oracle up to a multiplicative factor that depends on the number of actions. We also show that the other two popular estimators can be arbitrarily worse than the optimal, even in the limit of infinitely many data points. The performance of the estimators are studied in synthetic and real problems; illustrating the methods strengths and weaknesses. We also discuss the implications of these results for off-policy evaluation problems in contextual bandits and fixed-horizon Markov decision processes.<\/p>\n<\/div>\n<p><!-- .asset-content --><\/p>\n","protected":false},"excerpt":{"rendered":"<p>This paper studies the off-policy evaluation problem, where one aims to estimate the value of a target policy based on a sample of observations collected by another policy. We first consider the single-state, or multi-armed bandit case, establish a finite-time minimax risk lower bound, and analyze the risk of three standard estimators. For the so-called [&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":"","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-167936","msr-research-item","type-msr-research-item","status-publish","hentry","msr-research-area-artificial-intelligence","msr-locale-en_us"],"msr_publishername":"JMLR: Workshop and Conference Proceedings","msr_edition":"Proceedings of the 18th International Conference on Artificial Intelligence and Statistics (AISTATS)","msr_affiliation":"","msr_published_date":"2015-05-01","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_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":"204388","msr_publicationurl":"http:\/\/jmlr.org\/proceedings\/papers\/v38\/li15b.html","msr_doi":"","msr_publication_uploader":[{"type":"file","title":"li15b.pdf","viewUrl":"https:\/\/www.microsoft.com\/en-us\/research\/wp-content\/uploads\/2016\/02\/li15b.pdf","id":204388,"label_id":0},{"type":"url","title":"http:\/\/jmlr.org\/proceedings\/papers\/v38\/li15b.html","viewUrl":false,"id":false,"label_id":0}],"msr_related_uploader":"","msr_attachments":[{"id":0,"url":"http:\/\/jmlr.org\/proceedings\/papers\/v38\/li15b.html"},{"id":204388,"url":"https:\/\/www.microsoft.com\/en-us\/research\/wp-content\/uploads\/2016\/02\/li15b.pdf"}],"msr-author-ordering":[{"type":"user_nicename","value":"lihongli","user_id":32676,"rest_url":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/microsoft-research\/v1\/researchers?person=lihongli"},{"type":"text","value":"Remi Munos","user_id":0,"rest_url":false},{"type":"text","value":"Csaba Szepesvari","user_id":0,"rest_url":false}],"msr_impact_theme":[],"msr_research_lab":[],"msr_event":[],"msr_group":[],"msr_project":[171233],"publication":[],"video":[],"download":[],"msr_publication_type":"inproceedings","related_content":{"projects":[{"ID":171233,"post_title":"Explore-Exploit Learning @MSR-NYC","post_name":"explore-exploit-learning","post_type":"msr-project","post_date":"2013-10-24 16:52:27","post_modified":"2017-08-10 13:39:37","post_status":"publish","permalink":"https:\/\/www.microsoft.com\/en-us\/research\/project\/explore-exploit-learning\/","post_excerpt":"This is an umbrella project for machine learning with explore-exploit tradeoff: the trade-off between acquiring and using information. This is a mature, yet very active, research area studied in Machine Learning, Theoretical Computer Science, Operations Research, and Economics. Much of our activity focuses on \"multi-armed bandits\" and \"contextual bandits\", relatively simple and yet very powerful models for explore-exploit tradeoff. We are located in (or heavily collaborating with)\u00a0Microsoft Research New York City. Most of us are&hellip;","_links":{"self":[{"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-project\/171233"}]}}]},"_links":{"self":[{"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-research-item\/167936"}],"collection":[{"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-research-item"}],"about":[{"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/types\/msr-research-item"}],"version-history":[{"count":1,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-research-item\/167936\/revisions"}],"predecessor-version":[{"id":519478,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-research-item\/167936\/revisions\/519478"}],"wp:attachment":[{"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/media?parent=167936"}],"wp:term":[{"taxonomy":"msr-content-type","embeddable":true,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-content-type?post=167936"},{"taxonomy":"msr-research-highlight","embeddable":true,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-research-highlight?post=167936"},{"taxonomy":"msr-research-area","embeddable":true,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/research-area?post=167936"},{"taxonomy":"msr-publication-type","embeddable":true,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-publication-type?post=167936"},{"taxonomy":"msr-product-type","embeddable":true,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-product-type?post=167936"},{"taxonomy":"msr-focus-area","embeddable":true,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-focus-area?post=167936"},{"taxonomy":"msr-platform","embeddable":true,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-platform?post=167936"},{"taxonomy":"msr-download-source","embeddable":true,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-download-source?post=167936"},{"taxonomy":"msr-locale","embeddable":true,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-locale?post=167936"},{"taxonomy":"msr-post-option","embeddable":true,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-post-option?post=167936"},{"taxonomy":"msr-field-of-study","embeddable":true,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-field-of-study?post=167936"},{"taxonomy":"msr-conference","embeddable":true,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-conference?post=167936"},{"taxonomy":"msr-journal","embeddable":true,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-journal?post=167936"},{"taxonomy":"msr-impact-theme","embeddable":true,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-impact-theme?post=167936"},{"taxonomy":"msr-pillar","embeddable":true,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-pillar?post=167936"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}