On the computation of Whittle’s index for Markovian restless bandits

Urtzi Ayesta, Manu K. Gupta () and Ina Maria Verloop
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Urtzi Ayesta: Université de Toulouse, INP, 31071 Toulouse, France UPV/EHU, University of the Basque Country
Manu K. Gupta: Indian Institute of Technology Roorkee
Ina Maria Verloop: Université de Toulouse, INP

Mathematical Methods of Operations Research, 2021, vol. 93, issue 1, No 6, 179-208

Abstract: Abstract The multi-armed restless bandit framework allows to model a wide variety of decision-making problems in areas as diverse as industrial engineering, computer communication, operations research, financial engineering, communication networks etc. In a seminal work, Whittle developed a methodology to derive well-performing (Whittle’s) index policies that are obtained by solving a relaxed version of the original problem. However, the computation of Whittle’s index itself is a difficult problem and hence researchers focused on calculating Whittle’s index numerically or with a problem dependent approach. In our main contribution we derive an analytical expression for Whittle’s index for any Markovian bandit with both finite and infinite transition rates. We derive sufficient conditions for the optimal solution of the relaxed problem to be of threshold type, and obtain conditions for the bandit to be indexable, a property assuring the existence of Whittle’s index. Our solution approach provides a unifying expression for Whittle’s index, which we highlight by retrieving known indices from literature as particular cases. The applicability of finite rates is illustrated with the machine repairmen problem, and that of infinite rates by an example of communication networks where transmission rates react instantaneously to packet losses.

Keywords: Restless bandits; Whittle index; Impulse control (search for similar items in EconPapers)
Date: 2021
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Citations: View citations in EconPapers (2)

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DOI: 10.1007/s00186-020-00731-9

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