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The Knowledge Gradient (KG) policy was originally proposed for online rankingand selection problems but has recently been adapted for use in online decisionmaking in general and multi-armed bandit problems (MABs) in particular. Westudy its use in a class of exponential family MABs and identify weaknesses,including a propensity to take actions which are dominated with respect to bothexploitation and exploration. We propose variants of KG which avoid sucherrors. These new policies include an index heuristic which deploys a KGapproach to develop an approximation to the Gittins index. A numerical studyshows this policy to perform well over a range of MABs including those forwhich index policies are not optimal. While KG does not make dominated actionswhen bandits are Gaussian, it fails to be index consistent and appears not toenjoy a performance advantage over competitor policies when arms are correlatedto compensate for its greater computational demands.

On the Identification and Mitigation of Weaknesses in the Knowledge Gradient Policy for Multi-Armed Bandits