ASYMPTOTICALLY OPTIMAL MULTI-ARMED BANDIT POLICIES UNDER A COST CONSTRAINT
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Published:2016-10-05
Issue:3
Volume:31
Page:284-310
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ISSN:0269-9648
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Container-title:Probability in the Engineering and Informational Sciences
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language:en
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Short-container-title:Prob. Eng. Inf. Sci.
Author:
Burnetas Apostolos,Kanavetas Odysseas,Katehakis Michael N.
Abstract
We consider the multi-armed bandit problem under a cost constraint. Successive samples from each population are i.i.d. with unknown distribution and each sample incurs a known population-dependent cost. The objective is to design an adaptive sampling policy to maximize the expected sum ofnsamples such that the average cost does not exceed a given bound sample-path wise. We establish an asymptotic lower bound for the regret of feasible uniformly fast convergent policies, and construct a class of policies, which achieve the bound. We also provide their explicit form under Normal distributions with unknown means and known variances.
Publisher
Cambridge University Press (CUP)
Subject
Industrial and Manufacturing Engineering,Management Science and Operations Research,Statistics, Probability and Uncertainty,Statistics and Probability
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