  We consider the problem of best arm identification in a variant of
multi-armed bandits called linked bandits. In a single interaction with linked
bandits, multiple arms are played sequentially until one of them receives a
positive reward. Since each interaction provides feedback about more than one
arm, the sample complexity can be much lower than in the regular bandit
setting. We propose an algorithm for linked bandits, that combines a novel
subroutine to perform uniform sampling with a known optimal algorithm for
regular bandits. We prove almost matching upper and lower bounds on the sample
complexity of best arm identification in linked bandits. These bounds have an
interesting structure, with an explicit dependence on the mean rewards of the
arms, not just the gaps. We also corroborate our theoretical results with
experiments.
