Advances in Applied Probability

Index policies for discounted bandit problems with availability constraints

Savas Dayanik, Warren Powell, and Kazutoshi Yamazaki

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A multiarmed bandit problem is studied when the arms are not always available. The arms are first assumed to be intermittently available with some state/action-dependent probabilities. It is proven that no index policy can attain the maximum expected total discounted reward in every instance of that problem. The Whittle index policy is derived, and its properties are studied. Then it is assumed that the arms may break down, but repair is an option at some cost, and the new Whittle index policy is derived. Both problems are indexable. The proposed index policies cannot be dominated by any other index policy over all multiarmed bandit problems considered here. Whittle indices are evaluated for Bernoulli arms with unknown success probabilities.

Article information

Adv. in Appl. Probab. Volume 40, Number 2 (2008), 377-400.

First available in Project Euclid: 1 July 2008

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 93E20: Optimal stochastic control
Secondary: 90B36: Scheduling theory, stochastic [See also 68M20]

Optimal resource allocation multiarmed bandit problem Gittins index Whittle index restart-in problem


Dayanik, Savas; Powell, Warren; Yamazaki, Kazutoshi. Index policies for discounted bandit problems with availability constraints. Adv. in Appl. Probab. 40 (2008), no. 2, 377--400. doi:10.1239/aap/1214950209.

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