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Title of article :
On Gittins’ index theorem in continuous time
Author/Authors :
Bank، نويسنده , , Peter and Küchler، نويسنده , , Christian، نويسنده ,
Issue Information :
روزنامه با شماره پیاپی سال 2007
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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 :
Multi-armed bandits , Representation theorem , Gittins index
Journal title :
Stochastic Processes and their Applications
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Link To Document :