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Asymptotically optimal priority policies for indexable and nonindexable restless bandits

Verloop, Ina Maria Asymptotically optimal priority policies for indexable and nonindexable restless bandits. (2016) Annals of Applied Probability, vol. 26 (n° 4). pp. 1947-1995. ISSN 1050-5164

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Official URL: http://dx.doi.org/10.1214/15-AAP1137

Abstract

We study the asymptotic optimal control of multi-class restless bandits. A restless bandit is a controllable stochastic process whose state evolution depends on whether or not the bandit is made active. Since finding the optimal control is typically intractable, we propose a class of priority policies that are proved to be asymptotically optimal under a global attractor property and a technical condition. We consider both a fixed population of bandits as well as a dynamic population where bandits can depart and arrive. As an example of a dynamic population of bandits, we analyze a multi-class M/M/S+M queue for which we show asymptotic optimality of an index policy. We combine fluid-scaling techniques with linear programming results to prove that when bandits are indexable, Whittle's index policy is included in our class of priority policies. We thereby generalize a result of Weber and Weiss (1990) about asymptotic optimality of Whittle's index policy to settings with (i) several classes of bandits, (ii) arrivals of new bandits, and (iii) multiple actions. Indexability of the bandits is not required for our results to hold. For non-indexable bandits we describe how to select priority policies from the class of asymptotically optimal policies and present numerical evidence that, outside the asymptotic regime, the performance of our proposed priority policies is nearly optimal.

Item Type:Article
Additional Information:Thanks to Project Euclid. The definitive version is available at http://projecteuclid.org The original PDF of the article can be found at Annals of Applied Probability (1050-5164) website : http://projecteuclid.org/euclid.aoap/1472745449
Audience (journal):International peer-reviewed journal
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Institution:Université de Toulouse > Institut National Polytechnique de Toulouse - INPT (FRANCE)
French research institutions > Centre National de la Recherche Scientifique - CNRS (FRANCE)
Université de Toulouse > Université Toulouse III - Paul Sabatier - UPS (FRANCE)
Université de Toulouse > Université Toulouse - Jean Jaurès - UT2J (FRANCE)
Université de Toulouse > Université Toulouse 1 Capitole - UT1 (FRANCE)
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Deposited By: IRIT IRIT
Deposited On:06 Feb 2017 15:27

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