Adaptive Policies for Sequential Sampling under Incomplete Information   and a Cost Constraint
  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. 
Apostolos Burnetas and Odysseas Kanavetas
stat.ML cs.LG math.OC