Global Bandits

Standard multi-armed bandits model decision problems in which the consequences of each action choice are unknown and independent of each other. But in a wide variety of decision problems - from drug dosage to dynamic pricing - the consequences (rewards) of different actions are correlated, so that selecting one action provides information about the consequences (rewards) of other actions as well. We propose and analyze a class of models of such decision problems; we call this class of models global bandits. When rewards across actions (arms) are sufficiently correlated we construct a greedy policy that achieves bounded regret, with a bound that depends on the true parameters of the problem. In the special case in which rewards of all arms are deterministic functions of a single unknown parameter, we construct a (more sophisticated) greedy policy that achieves bounded regret, with a bound that depends on the single true parameter of the problem. For this special case we also obtain a bound on regret that is independent of the true parameter; this bound is sub-linear, with an exponent that depends on the informativeness of the arms (which measures the strength of correlation between arm rewards).