A convergent algorithm for ranking and selection with censored observations. (4th May 2023)

• Record Type: Journal Article
• Authors: Liu, Haitao; Xiao, Hui; Lee, Loo Hay; Chew, Ek Peng
• Is Part Of: IISE transactions. Volume 55:Number 5(2023)
• Page Start: 523
• Page End: 535
• Publication Date: 2023-05-04
• Subjects: Ranking and selection -- censored observations -- sequential sampling -- consistency -- asymptotic allocation; Industrial engineering -- Periodicals; Systems engineering -- Periodicals; Industrial engineering; Systems engineering; Electronic journals; Periodicals; 670.285
• DOI: 10.1080/24725854.2022.2055269
• Languages: English
• ISSNs: 2472-5854

Abstract

Abstract: We consider a problem of Ranking and Selection in the presence of Censored Observations (R&S-CO). An observation within the interval defined by lower and upper limits is observed at the actual value, whereas an observation outside the interval takes the closer limit value. The censored sample average is thus a biased estimator for the true mean performance of each alternative. The goal of R&S-CO is to efficiently find the best alternative in terms of the true mean. We first derive the censored variable's mean and variance in terms of the mean and variance of the uncensored variable and the lower and upper limits, and then develop a sequential sampling algorithm. Under mild conditions, we prove that the algorithm is consistent, in the sense that the best can be identified almost surely, as the sampling budget goes to infinity. Moreover, we show that the asymptotic allocation converges to the optimal static allocation derived by the large deviations theory. Extensive numerical experiments are conducted to investigate the finite-budget performance, the asymptotic allocation, and the robustness of the algorithm.