We consider an agent who has to repeatedly make choices in an uncertain and changing environment, who has full information of the past, who discounts future payoffs, but who has no prior. We provide a learning algorithm that performs almost as well as the best of a given finite number of experts...

A decision maker (DM) makes choices from different sets of alternatives. The DM is initially fully ignorant of the payoff associated to each alternative, and learns these payoffs only after a large number of choices have been made. We show that, in the presence of an outside option once payoffs...