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This paper studies the fixed budget formulation of the Ranking and Selection(R&S) problem with independent normal samples, where the goal is to investigatedifferent algorithms' convergence rate in terms of their resulting probabilityof false selection (PFS). First, we reveal that for the well-known OptimalComputing Budget Allocation (OCBA) algorithm and its two variants, a constantinitial sample size (independent of the total budget) only amounts to asub-exponential (or even polynomial) convergence rate. After that, amodification is proposed to achieve an exponential convergence rate, where theimprovement is shown by a finite-sample bound on the PFS as well as numericalresults. Finally, we focus on a more tractable two-design case and explicitlycharacterize the large deviations rate of PFS for some simplified algorithms.Our analysis not only develops insights into the algorithms' properties, butalso highlights several useful techniques for analyzing the convergence rate offixed budget R\&S algorithms.

Analyzing and provably improving fixed budget ranking and selection algorithms