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

TL;DR

This paper analyzes weaknesses in the Knowledge Gradient policy for multi-armed bandits, proposes improved variants, and evaluates their performance across different bandit settings.

Contribution

It identifies specific weaknesses in KG, introduces new variants including an index heuristic, and compares their effectiveness in various MAB scenarios.

Findings

KG can select dominated actions in some cases

New variants improve action selection accuracy

Performance varies depending on bandit correlation and complexity

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 make 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.