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Some reward–penalty rules for the multi-armed bandit problem which are asymptotically optimal

Published online by Cambridge University Press:  01 July 2016

K. D. Glazebrook
K. D. Glazebrook*
Affiliation:
University of Newcastle upon Tyne
*
∗Postal address: Department of Statistics, The University, Newcastle upon Tyne, NE1 7RU, U.K.
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Abstract

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In the mathematical learning literature, reward–penalty rules have been studied in various decision-theoretic and game-theoretic contexts, the multi-armed bandit problem included. Here we propose an elaboration of Bather's randomised allocation indices which yields rules for the multi-armed bandit which are both reward-penalty and asymptotically optimal.

Keywords

GITTINS INDEX: MATHEMATICAL LEARNING
Type
Letters to the Editor
Information
Advances in Applied Probability , Volume 15 , Issue 1 , March 1983 , pp. 221 - 222
Copyright
Copyright © Applied Probability Trust 1983 

References

Bather, J. (1980) Randomised allocation of treatments in sequential trials. Adv. Appl. Prob. 12, 174–182.Google Scholar
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Glazebrook, K. D. (1980) On randomized dynamic allocation indices for the sequential design of experiments. J. R. Statist. Soc., B42, 342–346.Google Scholar
Meybodi, M. R. and Lackshmivarahan, S. (1982) e-optimality of a general class of learning algorithms. In Proc. Conf. Mathematical Learning Models–Theory and Applications. To appear.Google Scholar