Vector optimization with stochastic bandit feedback
buir.contributor.author | Ararat, Çağın | |
buir.contributor.author | Tekin, Cem | |
buir.contributor.orcid | Ararat, Çağın|0000-0002-6985-7665 | |
buir.contributor.orcid | Tekin, Cem|0000-0003-4361-4021 | |
dc.citation.epage | 2190 | en_US |
dc.citation.spage | 2165 | |
dc.citation.volumeNumber | 206 | |
dc.contributor.author | Ararat, Çağın | |
dc.contributor.author | Tekin, Cem | |
dc.contributor.editor | Ruiz, F. | |
dc.contributor.editor | Dy J. | |
dc.contributor.editor | Van de Meent, J-W. | |
dc.coverage.spatial | Valencia, Spain | |
dc.date.accessioned | 2024-03-08T12:47:10Z | |
dc.date.available | 2024-03-08T12:47:10Z | |
dc.date.issued | 2023-03-07 | |
dc.department | Department of Industrial Engineering | |
dc.department | Department of Electrical and Electronics Engineering | |
dc.description | Conference Name: 26th International Conference on Artificial Intelligence and Statistics, AISTATS 2023 | |
dc.description | Date of Conference: 25 April 2023 - 27 April 2023 | |
dc.description.abstract | We 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.provenance | Made 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: 2023-03-07 | en |
dc.identifier.issn | 2640-3498 | |
dc.identifier.uri | https://hdl.handle.net/11693/114415 | |
dc.language.iso | en_US | |
dc.publisher | ML Research Press | |
dc.source.title | Proceedings of Machine Learning Research | |
dc.subject | Artificial intelligence | |
dc.subject | Budget control | |
dc.subject | Stochastic systems | |
dc.title | Vector optimization with stochastic bandit feedback | |
dc.type | Conference Paper |
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