Bandit problems with side observations

An extension of the traditional two-armed bandit problem is considered, in which the decision maker has access to some side information before deciding which arm to pull. At each time t, before making a selection, the decision maker is able to observe a random variable, X_t, that provides some information on the rewards to be obtained. The focus is on finding uniformly good rules (that minimize the growth rate or the regret) and on quantifying how much the additional information helps. Various settings are considered and asymptotically tight lower bounds on the achievable regret are provided.