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Some families of indexable restless bandit problems.

Glazebrook, Kevin and Kirkbride, C. and Ruiz-Hernandez, D. (2006) Some families of indexable restless bandit problems. Advances in Applied Probability, 38 (3). pp. 643-672. ISSN 1475-6064

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Abstract

In 1988 Whittle introduced an important but intractable class of restless bandit problems which generalise the multiarmed bandit problems of Gittins by allowing state evolution for passive projects. Whittle's account deployed a Lagrangian relaxation of the optimisation problem to develop an index heuristic. Despite a developing body of evidence (both theoretical and empirical) which underscores the strong performance of Whittle's index policy, a continuing challenge to implementation is the need to establish that the competing projects all pass an indexability test. In this paper we employ Gittins' index theory to establish the indexability of (inter alia) general families of restless bandits which arise in problems of machine maintenance and stochastic scheduling problems with switching penalties. We also give formulae for the resulting Whittle indices. Numerical investigations testify to the outstandingly strong performance of the index heuristics concerned.

Item Type: Article
Journal or Publication Title: Advances in Applied Probability
Additional Information: RAE_import_type : Journal article RAE_uoa_type : Statistics and Operational Research
Uncontrolled Keywords: Bandit problem ; dynamic programming ; Gittins index ; machine maintenance ; restless bandit ; stochastic scheduling ; switching cost
Subjects: Q Science > QA Mathematics
Departments: Faculty of Science and Technology > Mathematics and Statistics
ID Code: 2426
Deposited By: ep_importer
Deposited On: 31 Mar 2008 13:29
Refereed?: Yes
Published?: Published
Last Modified: 26 Jul 2012 16:23
Identification Number:
URI: http://eprints.lancs.ac.uk/id/eprint/2426

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