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Continuous-time allocation indices and their discrete-time approximation

Published online by Cambridge University Press:  01 July 2016

W. J. R. Eplett
W. J. R. Eplett*
Affiliation:
University of Oxford
*
∗Present address: Department of Statistics, University of Rochester, River Campus, Rochester, NY 14627, USA.
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Abstract

The theory of allocation indices for defining the optimal policy in multi-armed bandit problems developed by Gittins is presented in the continuous-time case where the projects (or ‘arms’) are strong Markov processes. Complications peculiar to the continuous-time case are discussed. This motivates investigation of whether approximation of the continuous-time problems by discrete-time versions provides a valid technique with convergent allocation indices and optimal expected rewards. Conditions are presented under which the convergence holds.

Keywords

MARKOV PROCESSESDYNAMIC ALLOCATION PROBLEMOPTIMAL STOPPINGCONVERGENCEDIFFUSIONS AND MARKOV CHAINS
Type
Research Article
Information
Advances in Applied Probability , Volume 18 , Issue 3 , September 1986 , pp. 724 - 746
Copyright
Copyright © Applied Probability Trust 1986 

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