  Multi-armed bandits (MAB) model sequential decision making problems, in which
a learner sequentially chooses arms with unknown reward distributions in order
to maximize its cumulative reward. Most of the prior work on MAB assumes that
the reward distributions of each arm are independent. But in a wide variety of
decision problems -- from drug dosage to dynamic pricing -- the expected
rewards of different arms are correlated, so that selecting one arm provides
information about the expected rewards of other arms as well. We propose and
analyze a class of models of such decision problems, which we call {\em global
bandits}. In the case in which rewards of all arms are deterministic functions
of a single unknown parameter, we construct a greedy policy that achieves {\em
bounded regret}, with a bound that depends on the single true parameter of the
problem. Hence, this policy selects suboptimal arms only finitely many times
with probability one. For this case we also obtain a bound on regret that is
{\em independent of the true parameter}; this bound is sub-linear, with an
exponent that depends on the informativeness of the arms. We also propose a
variant of the greedy policy that achieves $\tilde{\mathcal{O}}(\sqrt{T})$
worst-case and $\mathcal{O}(1)$ parameter dependent regret. Finally, we perform
experiments on dynamic pricing and show that the proposed algorithms achieve
significant gains with respect to the well-known benchmarks.
