Multi-objective multi-armed bandit with lexicographically ordered and satisficing objectives

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buir.contributor.authorTekin, Cem
buir.contributor.orcidTekin, Cem|0000-0003-4361-4021
dc.citation.epage1266en_US
dc.citation.spage1233en_US
dc.citation.volumeNumber110en_US
dc.contributor.authorHüyük, A.
dc.contributor.authorTekin, Cem
dc.date.accessioned2022-02-09T10:46:04Z
dc.date.available2022-02-09T10:46:04Z
dc.date.issued2021-06
dc.departmentDepartment of Electrical and Electronics Engineeringen_US
dc.description.abstractWe consider multi-objective multi-armed bandit with (i) lexicographically ordered and (ii) satisficing objectives. In the first problem, the goal is to select arms that are lexicographic optimal as much as possible without knowing the arm reward distributions beforehand. We capture this goal by defining a multi-dimensional form of regret that measures the loss due to not selecting lexicographic optimal arms, and then, propose an algorithm that achieves O~(T2/3) gap-free regret and prove a regret lower bound of Ω(T2/3). We also consider two additional settings where the learner has prior information on the expected arm rewards. In the first setting, the learner only knows for each objective the lexicographic optimal expected reward. In the second setting, it only knows for each objective a near-lexicographic optimal expected reward. For both settings, we prove that the learner achieves expected regret uniformly bounded in time. Then, we show that the algorithm we propose for the second setting of lexicographically ordered objectives with prior information also attains bounded regret for satisficing objectives. Finally, we experimentally evaluate the proposed algorithms in a variety of multi-objective learning problems.en_US
dc.description.provenanceSubmitted by Dilan Ayverdi (dilan.ayverdi@bilkent.edu.tr) on 2022-02-09T10:46:04Z No. of bitstreams: 1 Multi-objective_multi-armed_bandit_with_lexicographically_ordered_and_satisficing_objectives.pdf: 4005503 bytes, checksum: 227e126aecb4166503632494ae0bc863 (MD5)en
dc.description.provenanceMade available in DSpace on 2022-02-09T10:46:04Z (GMT). No. of bitstreams: 1 Multi-objective_multi-armed_bandit_with_lexicographically_ordered_and_satisficing_objectives.pdf: 4005503 bytes, checksum: 227e126aecb4166503632494ae0bc863 (MD5) Previous issue date: 2021-06en
dc.identifier.doi10.1007/s10994-021-05956-1en_US
dc.identifier.eissn1573-0565
dc.identifier.issn0885-6125
dc.identifier.urihttp://hdl.handle.net/11693/77165
dc.language.isoEnglishen_US
dc.publisherSpringeren_US
dc.relation.isversionofhttps://doi.org/10.1007/s10994-021-05956-1en_US
dc.source.titleMachine Learningen_US
dc.subjectMulti-armed banditen_US
dc.subjectMulti-objective learningen_US
dc.subjectLexicographic optimalityen_US
dc.subjectSatisficingen_US
dc.titleMulti-objective multi-armed bandit with lexicographically ordered and satisficing objectivesen_US
dc.typeArticleen_US

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