Adaptive fully sequential selection procedures with linear and nonlinear control variates

A decision-making process often involves selecting the best solution from a finite set of possible alternatives regarding some performance measure, which is known as Ranking-and-Selection (R&S) when the performance is not explicitly available and can only be estimated by taking samples. Many R&S procedures have been proposed considering different problem formulations. In this article, we adopt the classic fully sequential Indifference-Zone (IZ) formulation developed in the statistical literature, and take advantage of the control variates, a well-known variance reduction technique in the simulation literature, to investigate the potential benefits as well as the statistical guarantee by designing a new type of R&S procedure in an adaptive fashion. In particular, we propose a generic adaptive fully sequential procedure that can employ both linear and nonlinear control variates, in which both the control coefficient and sample variance can be sequentially updated as the sampling process progresses. We demonstrate that the proposed procedures provide the desired probability of correct selection in the asymptotic regime as the IZ parameter goes to zero. We then compare the proposed procedures with various existing procedures through the simulation experiments on practical illustrative examples, in which we observe several interesting findings and demonstrate the advantage of our proposed procedures.