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ON THE IDENTIFICATION AND MITIGATION OF WEAKNESSES IN THE KNOWLEDGE GRADIENT POLICY FOR MULTI-ARMED BANDITS

Published online by Cambridge University Press:  13 September 2016

James Edwards Open the ORCID record for James Edwards [Opens in a new window] ,
Paul Fearnhead  and
Kevin Glazebrook
James Edwards
Affiliation:
STOR-i Centre for Doctoral Training, Lancaster UniversityLancaster LA1 4YF, UK E-mail: j.edwards4@lancaster.ac.uk
Paul Fearnhead
Affiliation:
Department of Mathematics and Statistics, Lancaster University, Lancaster LA1 4YF, UK E-mail: p.fearnhead@lancaster.ac.uk
Kevin Glazebrook
Affiliation:
Department of Management Science, Lancaster University, Lancaster LA1 4YX, UK E-mail: k.glazebrook@lancaster.ac.uk
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Abstract

The knowledge gradient (KG) policy was originally proposed for online ranking and selection problems but has recently been adapted for use in online decision-making in general and multi-armed bandit problems (MABs) in particular. We study its use in a class of exponential family MABs and identify weaknesses, including a propensity to take actions which are dominated with respect to both exploitation and exploration. We propose variants of KG which avoid such errors. These new policies include an index heuristic, which deploys a KG approach to develop an approximation to the Gittins index. A numerical study shows this policy to perform well over a range of MABs including those for which index policies are not optimal. While KG does not take dominated actions when bandits are Gaussian, it fails to be index consistent and appears not to enjoy a performance advantage over competitor policies when arms are correlated to compensate for its greater computational demands.

Keywords

stochastic dynamic programming
Type
Research Article
Information
Probability in the Engineering and Informational Sciences , Volume 31 , Issue 2 , April 2017 , pp. 239 - 263
Copyright
Copyright © Cambridge University Press 2016 

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