Minimax and bates strategies for the discounted infinite horizon one-armed-bandit.—explicit formulae and structural properties

摘要

Summary. The discounted infinite horizon One-Armed-Bandit is considered. It is shown— neglecting overshoot—that the least favourable prior distribution has support on only two points. Further it is shown that the minimax strategy can be described by a straight line boundary. As long as the test statistic stays above this boundary, observations are taken, by crossing the boundary the procedure is stopped, The minimax strategy for the normal case is explicitly given as well as the corresponding minimax value. It is shown, that a large class of distributions has the same asymptotic strategy and the same asymptotic minimax value as the normal one for a ?1