Combined variance reduction techniques in fully sequential selection procedures

In the past several decades, many ranking-and-selection (R&S) procedures have been developed to select the best simulated system with the largest (or smallest) mean performance measure from a finite number of alternatives. A major issue to address in these R&S problems is to balance the trade-off between the effectiveness (ie, making a correct selection with a high probability) and the efficiency (ie, using a small total number of observations). In this paper, we take a frequentist's point of view by setting a predetermined probability of correct selection while trying to reduce the total sample size, that is, to improve the efficiency but also maintain the effectiveness. In particular, in order to achieve this goal, we investigate combining various variance reduction techniques into the fully sequential framework, resulting in different R&S procedures with either finite-time or asymptotic statistical validity. Extensive numerical experiments show great improvement in the efficiency of our proposed procedures as compared with several existing procedures.