Title:

The (Surprising) Rate Optimality of Greedy Procedures for Large-Scale Ranking and Selection

Abstract:

Ranking and selection (R&S) aims to select the best alternative with the largest mean performance from a finite set of alternatives. Recently, considerable attention has turned toward the large-scale R&S problem which involves a large number of alternatives. Ideal large-scale R&S procedures should be sample optimal; that is, the total sample size required to deliver an asymptotically nonzero probability of correct selection (PCS) grows at the minimal order (linear order) in the number of alternatives, k. Surprisingly, we discover that the naïve 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 sample optimal for the scenarios where the best mean maintains at least a positive constant away from all other means as k increases. We further show that the derived PCS lower bound is asymptotically tight for the slippage configuration of means with a common variance. For other scenarios, we consider the probability of good selection and find that the result depends on the growth behavior of the number of good alternatives: if it remains bounded as k increases, the sample optimality still holds; otherwise, the result may change. Moreover, we propose the explore-first greedy procedures by adding an exploration phase to the greedy procedure. The procedures are proven to be sample optimal and consistent under the same assumptions. Last, we numerically investigate the performance of our greedy procedures in solving large-scale R&S problems.

This is a joint work with Zaile Li at INSEAD and Weiwei Fan at Tongji University. The paper is available at https://doi.org/10.1287/mnsc.2023.00694.

Bio:

Jeff Hong received his bachelor’s degree from Tsinghua University and his Ph.D. from Northwestern University. He is currently a professor in the Department of Industrial and Systems Engineering at the University of Minnesota, Twin Cities. Previously, he held faculty positions at Fudan University, the City University of Hong Kong, and the Hong Kong University of Science and Technology. His research interests include stochastic simulation, stochastic optimization, risk management, and supply chain management. Jeff is the Simulation Department Editor of Naval Research Logistics and an Associate Editor for Management Science and ACM Transactions on Modeling and Computer Simulation. He served as the Simulation Area Editor for Operations Research from 2018 to 2023, and as President of the INFORMS Simulation Society from 2020 to 2022.