A Fully Sequential Elimination Procedure for Indi↵erence-Zone Ranking and Selection with Tight Bounds on Probability of Correct Selection

We consider the indi↵erence-zone (IZ) formulation of the ranking and selection problem with independent normal samples. In this problem, we must use stochastic simulation to select the best among several noisy simulated systems, with a statistical guarantee on solution quality. Existing IZ procedures sample excessively in problems with many alternatives, in part because loose bounds on probability of correct selection lead them to deliver solution quality much higher than requested. Consequently, existing IZ procedures are seldom considered practical for problems with more than a few hundred alternatives. To overcome this, we present a new sequential elimination IZ procedure, called BIZ (Bayes-inspired Indi↵erence Zone), whose lower bound on worst-case probability of correct selection in the preference zone is tight in continuous time, and nearly tight in discrete time. To the author’s knowledge, this is the first sequential elimination procedure with tight bounds on worst-case preference-zone probability of correct selection for more than two alternatives. Theoretical results for the discrete-time case assume that variances are known and have an integer multiple structure, but the BIZ procedure itself can be used when these assumptions are not met. In numerical experiments, the sampling e↵ort used by BIZ is significantly smaller than that of another leading IZ procedure, the KN procedure of Kim and Nelson (2001), especially on the largest problems tested (2 = 16,384 alternatives).