On the Identification and Mitigation of Weaknesses in the Knowledge Gradient Policy for Multi-Armed Bandits
This work addresses performance issues in decision-making policies for multi-armed bandits, offering incremental improvements for researchers and practitioners in online optimization.
The paper identifies weaknesses in the Knowledge Gradient (KG) policy for multi-armed bandits, such as taking dominated actions in exponential family MABs, and proposes variants that avoid these errors, including an index heuristic approximating the Gittins index, which performs well in numerical studies across various MABs.
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.