We address the problem of designing a tractable, well-grounded policy for the dynamic allocation of effort to a collection of restless bandit projects, i.e. binary-action (active/passive) Markov decision processes, in which sequence-independent switching penalties (costs or delays) are incurred when switching from one project to another. We deploy the framework of partial conservation laws, introduced by Ni�±o-Mora (2001, 2002), to establish the existence of and calculate a marginal productivity index (MPI), under certain conditions. The MPI, which extends earlier indices proposed by Gittins (1979) and Whittle (1988), yields a corresponding MPI policy, which prescribes to dynamically engage the project with larger index.
@InProceedings{ninomora:DagSemProc.05031.13, author = {Ni\~{n}o-Mora, Jos\'{e}}, title = {{Marginal productivity index policies for scheduling restless bandits with switching penalties}}, booktitle = {Algorithms for Optimization with Incomplete Information}, pages = {1--6}, series = {Dagstuhl Seminar Proceedings (DagSemProc)}, ISSN = {1862-4405}, year = {2005}, volume = {5031}, editor = {Susanne Albers and Rolf H. M\"{o}hring and Georg Ch. Pflug and R\"{u}diger Schultz}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/DagSemProc.05031.13}, URN = {urn:nbn:de:0030-drops-644}, doi = {10.4230/DagSemProc.05031.13}, annote = {Keywords: stochastic scheduling , restless bandits , index policies , switching penalties} }
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