We study contextual combinatorial bandits with probabilistically triggered arms (C\\(^2\\)MAB-T) under a variety of smoothness conditions that capture a wide range of applications, such as contextual cascading bandits and contextual influence maximization bandits. Under the triggering probability modulated (TPM) condition, we devise the C\\(^2\\)-UCB-T algorithm and propose a novel analysis that achieves an \\(\\tilde{O}(d\\sqrt{KT})\\) regret bound, removing a potentially exponentially large factor \\(O(1\/p_{min})\\), where \\(d\\) is the dimension of contexts, \\(p_{min}\\) is the minimum positive probability that any arm can be triggered, and batch-size \\(K\\) is the maximum number of arms that can be triggered per round. Under the variance modulated (VM) or triggering probability and variance modulated (TPVM) conditions, we propose a new variance-adaptive algorithm VAC\\(^2\\)-UCB and derive a regret bound \\(\\tilde{O}(d\\sqrt{T})\\), which is independent of the batch-size \\(K\\). As a valuable by-product, we find our analysis technique and variance-adaptive algorithm can be applied to the CMAB-T and C\\(^2\\)MAB setting, improving existing results there as well. We also include experiments that demonstrate the improved performance of our algorithms compared with benchmark algorithms on synthetic and real-world datasets.<\/p>\n","protected":false},"excerpt":{"rendered":"
We study contextual combinatorial bandits with probabilistically triggered arms (CMAB-T) under a variety of smoothness conditions that capture a wide range of applications, such as contextual cascading bandits and contextual influence maximization bandits. Under the triggering probability modulated (TPM) condition, we devise the C-UCB-T algorithm and propose a novel analysis that achieves an regret bound, […]<\/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-946008","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":"2023-7-1","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":"file","viewUrl":"https:\/\/www.microsoft.com\/en-us\/research\/uploads\/prod\/2023\/06\/ICML2023_CCMABT.pdf","id":"948729","title":"icml2023_ccmabt","label_id":"243132","label":0},{"type":"url","viewUrl":"false","id":"false","title":"https:\/\/arxiv.org\/abs\/2303.17110","label_id":"252679","label":0}],"msr_related_uploader":"","msr_attachments":[{"id":948729,"url":"https:\/\/www.microsoft.com\/en-us\/research\/uploads\/prod\/2023\/06\/ICML2023_CCMABT.pdf"}],"msr-author-ordering":[{"type":"text","value":"Xutong Liu","user_id":0,"rest_url":false},{"type":"text","value":"Jinhang Zuo","user_id":0,"rest_url":false},{"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":"John C.S. 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