Solving Large-Scale Fixed-Budget Ranking and Selection Problems

In recent years, with the rapid development of computing technology, developing parallel procedures to solve large-scale ranking and selection (R&S) problems has attracted a lot of research attention. In this paper, we take fixed-budget R&S procedure as an example to investigate potential issues of developing parallel procedures. We argue that to measure the performance of a fixed-budget R&S procedure in solving large-scale problems, it is important to quantify the minimal growth rate of the total sampling budget such that as the number of alternatives increases, the probability of correct selection (PCS) would not decrease to zero. We call such a growth rate of the total sampling budget the rate for maintaining correct selection (RMCS). We show that a tight lower bound for the RMCS of a broad class of existing fixed-budget procedures is in the order of k logk, where k is the number of alternatives. Then, we propose a new type of fixed-budget procedure, namely the fixed-budget knockout-tournament (FBKT) procedure. We prove that, in terms of the RMCS, our procedure outperforms existing fixed-budget procedures and achieves the optimal order, that is, the order of k. Moreover, we demonstrate that our procedure can be easily implemented in parallel computing environments with almost no nonparallelizable calculations. Last, a comprehensive numerical study shows that our procedure is indeed suitable for solving large-scale problems in parallel computing environments.

Automated summary

This paper investigates the potential issues of developing parallel procedures to solve large-scale ranking and selection (R&S) problems. A new type of fixed-budget procedure, called the fixed-budget knockout-tournament (FBKT) procedure, is proposed and shown to outperform existing fixed-budget procedures in terms of maintaining correct selection. The procedure is also shown to be suitable for solving large-scale problems in parallel computing environments.