Adaptive Policies for Sequential Sampling under Incomplete Information and a Cost Constraint

Abstract: We consider the problem of sequential sampling from a finite number of independent statistical populations to maximize the expected infinite horizon average outcome per period, under a constraint that the expected average sampling cost does not exceed an upper bound. The outcome distributions are not known. We construct a class of consistent adaptive policies, under which the average outcome converges with probability 1 to the true value under complete information for all distributions with finite means. We also compare the rate of convergence for various policies in this class using simulation.