Vector optimization with stochastic bandit feedback

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buir.contributor.authorArarat, Çağın
buir.contributor.authorTekin, Cem
buir.contributor.orcidArarat, Çağın|0000-0002-6985-7665
buir.contributor.orcidTekin, Cem|0000-0003-4361-4021
dc.citation.epage2190en_US
dc.citation.spage2165
dc.citation.volumeNumber206
dc.contributor.authorArarat, Çağın
dc.contributor.authorTekin, Cem
dc.contributor.editorRuiz, F.
dc.contributor.editorDy J.
dc.contributor.editorVan de Meent, J-W.
dc.coverage.spatialValencia, Spain
dc.date.accessioned2024-03-08T12:47:10Z
dc.date.available2024-03-08T12:47:10Z
dc.date.issued2023-03-07
dc.departmentDepartment of Industrial Engineering
dc.departmentDepartment of Electrical and Electronics Engineering
dc.descriptionConference Name: 26th International Conference on Artificial Intelligence and Statistics, AISTATS 2023
dc.descriptionDate of Conference: 25 April 2023 - 27 April 2023
dc.description.abstractWe introduce vector optimization problems with stochastic bandit feedback, in which preferences among designs are encoded by a polyhedral ordering cone C. Our setup generalizes the best arm identification problem to vector-valued rewards by extending the concept of Pareto set beyond multi-objective optimization. We characterize the sample complexity of (ϵ, δ)-PAC Pareto set identification by defining a new cone-dependent notion of complexity, called the ordering complexity. In particular, we provide gap-dependent and worst-case lower bounds on the sample complexity and show that, in the worst-case, the sample complexity scales with the square of ordering complexity. Furthermore, we investigate the sample complexity of the naïve elimination algorithm and prove that it nearly matches the worst-case sample complexity. Finally, we run experiments to verify our theoretical results and illustrate how C and sampling budget affect the Pareto set, the returned (ϵ, δ)-PAC Pareto set, and the success of identification. Copyright © 2023 by the author(s)
dc.description.provenanceMade available in DSpace on 2024-03-08T12:47:10Z (GMT). No. of bitstreams: 1 Vector_optimization_with_stochastic_bandit_feedback.pdf: 632722 bytes, checksum: 75f4cef9a65f5f912b89f06d92914a22 (MD5) Previous issue date: 2023-03-07en
dc.identifier.issn2640-3498
dc.identifier.urihttps://hdl.handle.net/11693/114415
dc.language.isoen_US
dc.publisherML Research Press
dc.source.titleProceedings of Machine Learning Research
dc.subjectArtificial intelligence
dc.subjectBudget control
dc.subjectStochastic systems
dc.titleVector optimization with stochastic bandit feedback
dc.typeConference Paper

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