On Finding the Largest Mean Among Many

Understand

Sampling from distributions to find the one with the largest mean arises in a broad range of applications, and it can be mathematically modeled as a multi-armed bandit problem in which each distribution is associated with an arm.

• This paper studies the sample complexity of identifying the best arm (largest mean) in a multi-armed bandit problem.
• Motivated by large-scale applications, we are especially interested in identifying situations where the total number of samples that are necessary and sufficient to find the best arm scale linearly with the number of arms.
• We present a single-parameter multi-armed bandit model that spans the range from linear to superlinear sample complexity.