Restless Bandits, Partial Conservation Laws and Indexability

UPF Economics and Business Working Paper No. 435

34 Pages Posted: 1 May 2000

See all articles by José Niño Mora

José Niño Mora

Universitat Pompeu Fabra - Faculty of Economic and Business Sciences

Abstract

We show that if performance measures in a stochastic scheduling problem satisfy a set of so-called partial conservation laws (PCL), which extend previously studied generalized conservation laws (GCL), then the problem is solved optimally by a priority-index policy for an appropriate range of linear performance objectives, where the optimal indices are computed by a one-pass adaptive-greedy algorithm, based on Klimov's. We further apply this framework to investigate the indexability property of restless bandits introduced by Whittle, obtaining the following results: (1) we identify a class of restless bandits (PCL-indexable) which are indexable; membership in this class is tested through a single run of the adaptive-greedy algorithm, which also computes the Whittle indices when the test is positive; this provides a tractable sufficient condition for indexability; (2) we further indentify the class of GCL-indexable bandits, which includes classical bandits, having the property that they are indexable under any linear reward objective. The analysis is based on the so-called achievable region method, as the results follow from new linear programming formulations for the problems investigated.

JEL Classification: C60, C61

Suggested Citation

Niño Mora, José, Restless Bandits, Partial Conservation Laws and Indexability. UPF Economics and Business Working Paper No. 435, Available at SSRN: https://ssrn.com/abstract=224565 or http://dx.doi.org/10.2139/ssrn.224565

José Niño Mora (Contact Author)

Universitat Pompeu Fabra - Faculty of Economic and Business Sciences ( email )

Ramon Trias Fargas 25-27
Barcelona, 08005
Spain
(34-3) 542 26 73 (Phone)
(34-3) 542 17 46 (Fax)

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