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Gaussian Process Classification Bandits

Tatsuya HayashiNaoki ItoKoji Tabata ...+3 Tamiki Komatsuzaki
Dec 2022
摘要
Classification bandits are multi-armed bandit problems whose task is toclassify a given set of arms into either positive or negative class dependingon whether the rate of the arms with the expected reward of at least h is notless than w for given thresholds h and w. We study a special classificationbandit problem in which arms correspond to points x in d-dimensional real spacewith expected rewards f(x) which are generated according to a Gaussian processprior. We develop a framework algorithm for the problem using various armselection policies and propose policies called FCB and FTSV. We show a smallersample complexity upper bound for FCB than that for the existing algorithm ofthe level set estimation, in which whether f(x) is at least h or not must bedecided for every arm's x. Arm selection policies depending on an estimatedrate of arms with rewards of at least h are also proposed and shown to improveempirical sample complexity. According to our experimental results, therate-estimation versions of FCB and FTSV, together with that of the popularactive learning policy that selects the point with the maximum variance,outperform other policies for synthetic functions, and the version of FTSV isalso the best performer for our real-world dataset.
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