We consider high dimensional dynamic multi-product pricing with an evolving but low-dimensional linear demand model. Assuming the temporal variation in cross-elasticities exhibits low-rank structure based on fixed (latent) features of the products, we show that the revenue maximization problem reduces to an online bandit convex optimization with side information given by the observed demands. We design dynamic pricing algorithms whose revenue approaches that of the best fixed price vector in hindsight, at a rate that only depends on the intrinsic rank of the demand model and not the number of products. Our approach applies a bandit convex optimization algorithm in a projected low-dimensional space spanned by the latent product features, while simultaneously learning this span via online singular value decomposition of a carefully-crafted matrix containing the observed demands.<\/p>\n","protected":false},"excerpt":{"rendered":"
We consider high dimensional dynamic multi-product pricing with an evolving but low-dimensional linear demand model. Assuming the temporal variation in cross-elasticities exhibits low-rank structure based on fixed (latent) features of the products, we show that the revenue maximization problem reduces to an online bandit convex optimization with side information given by the observed demands. We […]<\/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":[13548],"msr-publication-type":[193715],"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-471504","msr-research-item","type-msr-research-item","status-publish","hentry","msr-research-area-economics","msr-locale-en_us"],"msr_publishername":"","msr_edition":"","msr_affiliation":"","msr_published_date":"2019-9-11","msr_host":"","msr_duration":"","msr_version":"","msr_speaker":"","msr_other_contributors":"","msr_booktitle":"","msr_pages_string":"","msr_chapter":"","msr_isbn":"","msr_journal":"arXiv","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\/pdf\/1801.10242%20","msr_doi":"","msr_publication_uploader":[{"type":"url","viewUrl":"false","id":"false","title":"https:\/\/arxiv.org\/pdf\/1801.10242%20","label_id":"243109","label":0}],"msr_related_uploader":"","msr_attachments":[{"id":0,"url":"https:\/\/arxiv.org\/pdf\/1801.10242%20"}],"msr-author-ordering":[{"type":"text","value":"Jonas Mueller","user_id":0,"rest_url":false},{"type":"user_nicename","value":"Vasilis Syrgkanis","user_id":34499,"rest_url":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/microsoft-research\/v1\/researchers?person=Vasilis Syrgkanis"},{"type":"text","value":"Matt Taddy","user_id":0,"rest_url":false}],"msr_impact_theme":[],"msr_research_lab":[199563],"msr_event":[],"msr_group":[437316,656316],"msr_project":[656325,332666],"publication":[],"video":[],"download":[],"msr_publication_type":"article","related_content":{"projects":[{"ID":656325,"post_title":"EconML","post_name":"econml","post_type":"msr-project","post_date":"2020-06-02 09:40:48","post_modified":"2022-02-24 07:11:27","post_status":"publish","permalink":"https:\/\/www.microsoft.com\/en-us\/research\/project\/econml\/","post_excerpt":"EconML\u00a0is an open source Python package developed by the ALICE team at Microsoft Research that applies the power of machine learning techniques to estimate individualized causal responses from observational or experimental data. 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