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We consider a novel multi-armed bandit framework where the rewards obtainedby pulling the arms are functions of a common latent random variable. Thecorrelation between arms due to the common random source can be used to designa generalized upper-confidence-bound (UCB) algorithm that identifies certainarms 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 thebest arm and $C$ $competitive$ arms. Our regret analysis shows that thecompetitive arms need to be pulled $\mathcal{O}(\log T)$ times, while thenon-competitive arms are pulled only $\mathcal{O}(1)$ times. As a result, thereare regimes where our algorithm achieves a $\mathcal{O}(1)$ regret as opposedto the typical logarithmic regret scaling of multi-armed bandit algorithms. Wealso evaluate lower bounds on the expected regret and prove that ourcorrelated-UCB algorithm achieves $\mathcal{O}(1)$ regret whenever possible.

Correlated Multi-armed Bandits with a Latent Random Source