# Three Asymptotic Regimes for Ranking and Selection with General Sample Distributions

## TL;DR

This paper investigates three asymptotic regimes for ranking and selection problems with general distributions, establishing their validity, efficiency, and interconnections, and comparing algorithm performances in these regimes.

## Contribution

It introduces and analyzes three novel asymptotic regimes for R&S with general distributions, providing theoretical validation and performance comparisons.

## Key findings

- Asymptotic regimes are valid and efficient for R&S.
- Connections among different regimes are characterized.
- Pre-limit algorithm performances are compared.

## Abstract

In this paper, we study three asymptotic regimes that can be applied to ranking and selection (R&S) problems with general sample distributions. These asymptotic regimes are constructed by sending particular problem parameters (probability of incorrect selection, smallest difference in system performance that we deem worth detecting) to zero. We establish asymptotic validity and efficiency of the corresponding R&S procedures in each regime. We also analyze the connection among different regimes and compare the pre-limit performances of corresponding algorithms.