  We study the bandit problem where arms are associated with stationary
phi-mixing processes and where rewards are therefore dependent: the question
that arises from this setting is that of recovering some independence by
ignoring the value of some rewards. As we shall see, the bandit problem we
tackle requires us to address the exploration/exploitation/independence
trade-off. To do so, we provide a UCB strategy together with a general regret
analysis for the case where the size of the independence blocks (the ignored
rewards) is fixed and we go a step beyond by providing an algorithm that is
able to compute the size of the independence blocks from the data. Finally, we
give an analysis of our bandit problem in the restless case, i.e., in the
situation where the time counters for all mixing processes simultaneously
evolve.
