Correlated Multi-armed Bandits with a Latent Random Source

We consider a novel multi-armed bandit framework where the rewards obtained by pulling the arms are functions of a common latent random variable. The correlation between arms due to the common random source can be used to design a generalized upper-confidence-bound (UCB) algorithm that identifies certain arms as non-competitive, and avoids exploring them. As a result, we reduce a K-armed bandit problem to a C+1-armed problem, where C+1 includes the best arm and C competitive arms. Our regret analysis shows that the competitive arms need to be pulled O(log T) times, while the non-competitive arms are pulled only O(1) times. As a result, there are regimes where our algorithm achieves a O(1) regret as opposed to the typical logarithmic regret scaling of multi-armed bandit algorithms. We also evaluate lower bounds on the expected regret and prove that our correlated-UCB algorithm achieves O(1) regret whenever possible.