Large-scale ranking and selection (R&S), which aims to select the best alternative with the largest mean performance from a finite set of alternatives, has emerged as an important research topic in simulation optimization. Ideal large-scale R&S procedures should be rate optimal, i.e., the total sample size required to deliver an asymptotically non-zero probability of correct selection (PCS) grows at the minimal rate (linear rate) in the number of alternatives. Surprisingly, we discover that the na\"ive greedy procedure that keeps sampling the alternative with the largest running average performs strikingly well and appears rate optimal. To understand this discovery, we develop a new boundary-crossing perspective and prove that the greedy procedure is indeed rate 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 ($\mbox{EFG}^+$ procedure) by adding an exploration phase to the na\"ive greedy procedure. Both procedures are proven to be rate 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：大规模排序与选择旨在从有限备选方案中选出均值性能最优的方案，已成为仿真优化领域的重要研究方向。理想的大规模排序与选择过程应具备最优收敛速率，即实现渐近非零的正确选择概率所需的总样本量随备选方案数量呈最小速率（线性速率）增长。令人惊讶的是，我们发现在采样过程中持续选择当前运行均值最大的备选方案的朴素贪心过程表现极为优异，且似乎具有最优收敛速率。为理解这一发现，我们提出新的边界穿越视角，并证明贪心过程确实具有最优收敛速率。进一步研究表明，在均值滑动配置且方差齐性的条件下，所推导的正确选择概率下界是渐近紧的。此外，我们提出先探索后贪心过程及其增强版本，通过向朴素贪心过程添加探索阶段实现。两种过程均被证明具有最优收敛速率与一致性。最后，通过大量数值实验实证分析了贪心过程在解决大规模排序与选择问题中的性能表现。