On Gittins' index theorem in continuous time

Peter Bank and Christian Küchler

Stochastic Processes and their Applications, 2007, vol. 117, issue 9, 1357-1371

Abstract: We give a new and comparably short proof of Gittins' index theorem for dynamic allocation problems of the multi-armed bandit type in continuous time under minimal assumptions. This proof gives a complete characterization of optimal allocation strategies as those policies which follow the current leader among the Gittins indices while ensuring that a Gittins index is at an all-time low whenever the associated project is not worked on exclusively. The main tool is a representation property of Gittins index processes which allows us to show that these processes can be chosen to be pathwise lower semi-continuous from the right and quasi-lower semi-continuous from the left. Both regularity properties turn out to be crucial for our characterization and the construction of optimal allocation policies.

Keywords: Gittins; index; Multi-armed; bandits; Representation; theorem (search for similar items in EconPapers)
Date: 2007
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Citations: View citations in EconPapers (3)

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