  We study a variant of the classical multi-armed bandit problem (MABP) which
we call as Multi-Armed Bandits with dependent arms. More specifically, multiple
arms are grouped together to form a cluster, and the reward distributions of
arms belonging to the same cluster are known functions of an unknown parameter
that is a characteristic of the cluster. Thus, pulling an arm $i$ not only
reveals information about its own reward distribution, but also about all those
arms that share the same cluster with arm $i$. This "correlation" amongst the
arms complicates the exploration-exploitation trade-off that is encountered in
the MABP because the observation dependencies allow us to test simultaneously
multiple hypotheses regarding the optimality of an arm. We develop learning
algorithms based on the UCB principle which utilize these additional side
observations appropriately while performing exploration-exploitation trade-off.
We show that the regret of our algorithms grows as $O(K\log T)$, where $K$ is
the number of clusters. In contrast, for an algorithm such as the vanilla UCB
that is optimal for the classical MABP and does not utilize these dependencies,
the regret scales as $O(M\log T)$ where $M$ is the number of arms.
