Ranking and selection (R&S), which aims to select the best alternative with the largest mean performance from a finite set of alternatives, is a classic research topic in simulation optimization. Recently, considerable attention has turned towards the large-scale variant of the R&S problem which involves a large number of alternatives. Ideal large-scale R&S procedures should be sample optimal, i.e., the total sample size required to deliver an asymptotically non-zero probability of correct selection (PCS) grows at the minimal order (linear order) in the number of alternatives, but not many procedures in the literature are sample optimal. Surprisingly, we discover that the na\"ive greedy procedure, which keeps sampling the alternative with the largest running average, performs strikingly well and appears sample optimal. To understand this discovery, we develop a new boundary-crossing perspective and prove that the greedy procedure is indeed sample optimal. We further show that the derived PCS lower bound is asymptotically tight for the slippage configuration of means with a common variance. Moreover, we propose the explore-first greedy (EFG) procedure and its enhanced version (EFG$^+$ procedure) by adding an exploration phase to the na\"ive greedy procedure. Both procedures are proven to be sample optimal and consistent. Last, we conduct extensive numerical experiments to empirically understand the performance of our greedy procedures in solving large-scale R&S problems.

翻译：排序与选择（R&S）旨在从有限候选项中选出均值性能最优的最佳方案，是仿真优化领域的经典研究方向。近年来，涉及大量候选项的大规模R&S问题受到广泛关注。理想的大规模R&S过程应具有样本最优性，即确保渐近非零正确选择概率（PCS）所需的总样本量随候选项数量呈最小阶（线性阶）增长，但现有文献中符合样本最优性的过程并不多见。令人惊讶的是，我们发现朴素贪婪过程——即持续采样当前运行均值最大的候选项——表现极为出色，且具有样本最优性。为理解这一发现，我们提出了一种新的边界穿越视角，并证明贪婪过程确实具有样本最优性。进一步研究表明，针对具有公共方差的均值偏移配置，所推导的PCS下界是渐近紧致的。此外，我们通过为朴素贪婪过程增加探索阶段，提出了先探索后贪婪（EFG）过程及其增强版本（EFG+过程）。这两个过程均被证明具有样本最优性和一致性。最后，我们通过大量数值实验实证了贪婪过程在求解大规模R&S问题中的性能表现。