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The multi-armed bandit problem with covariates

Author(s): Perchet, Vianney; Rigollet, Philippe

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dc.contributor.authorPerchet, Vianney-
dc.contributor.authorRigollet, Philippe-
dc.date.accessioned2020-03-23T18:18:31Z-
dc.date.available2020-03-23T18:18:31Z-
dc.date.issued2013-04en_US
dc.identifier.citationPerchet, Vianney, Rigollet, Philippe. (2013). The multi-armed bandit problem with covariates. The Annals of Statistics, 41 (2), 693 - 721. doi:10.1214/13-AOS1101en_US
dc.identifier.issn0090-5364-
dc.identifier.urihttp://arks.princeton.edu/ark:/88435/pr1kj64-
dc.description.abstractWe consider a multi-armed bandit problem in a setting where each arm produces a noisy reward realization which depends on an observable random covariate. As opposed to the traditional static multi-armed bandit problem, this setting allows for dynamically changing rewards that better describe applications where side information is available. We adopt a nonparametric model where the expected rewards are smooth functions of the covariate and where the hardness of the problem is captured by a margin parameter. To maximize the expected cumulative reward, we introduce a policy called Adaptively Binned Successive Elimination (ABSE) that adaptively decomposes the global problem into suitably “localized” static bandit problems.This policy constructs an adaptive partition using a variant of the Successive Elimination (SE) policy. Our results include sharper regret bounds for the SE policy in a static bandit problem and minimax optimal regret bounds for the ABSE policy in the dynamic problem.en_US
dc.format.extent693 - 721en_US
dc.language.isoen_USen_US
dc.relation.ispartofThe Annals of Statisticsen_US
dc.rightsFinal published version. Article is made available in OAR by the publisher's permission or policy.en_US
dc.titleThe multi-armed bandit problem with covariatesen_US
dc.typeJournal Articleen_US
dc.identifier.doidoi:10.1214/13-AOS1101-
pu.type.symplectichttp://www.symplectic.co.uk/publications/atom-terms/1.0/journal-articleen_US

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