Asymptotic Optimality of Myopic Ranking and Selection Procedures

TL;DR

This paper proves that simple myopic ranking and selection procedures are asymptotically optimal, explaining their strong empirical performance and providing insights into the theoretical foundations of efficient R&S methods.

Contribution

It offers a theoretical proof that myopic R&S procedures satisfy optimality conditions, bridging the gap between empirical success and theoretical justification.

Findings

Myopic procedures are asymptotically optimal.

They perform competitively with more complex methods.

Theoretical analysis explains their empirical effectiveness.

Abstract

Ranking and selection (R&S) is a popular model for studying discrete-event dynamic systems. It aims to select the best design (the design with the largest mean performance) from a finite set, where the mean of each design is unknown and has to be learned by samples. Great research efforts have been devoted to this problem in the literature for developing procedures with superior empirical performance and showing their optimality. In these efforts, myopic procedures were popular. They select the best design using a 'naive' mechanism of iteratively and myopically improving an approximation of the objective measure. Although they are based on simple heuristics and lack theoretical support, they turned out highly effective, and often achieved competitive empirical performance compared to procedures that were proposed later and shown to be asymptotically optimal. In this paper, we theoretically analyze these myopic procedures and prove that they also satisfy the optimality conditions of R&S, just like some other popular R&S methods. It explains the good performance of myopic procedures in various numerical tests, and provides good insight into the structure and theoretical development of efficient R&S procedures.