Sequential Learning with a Similarity Selection Index

We consider the problem of selecting the best alternative in a setting where prior similarity information between the performance output of different alternatives can be learned from data. Incorporating similarity information enables efficient budget allocation for faster identification of the best alternative in sequential selection. Using a new selection criterion, the similarity selection index, we develop two new allocation methods: one based on a mathematical programming characterization of the asymptotically optimal budget allocation and the other based on a myopic expected improvement measure. For the former, we present a novel sequential implementation that provably learns the optimal allocation without tuning. For the latter, we derive its asymptotic sampling ratios. We also propose a practical way to update the prior similarity information as new samples are collected. Numerical results illustrate the effectiveness of both methods.

Funding: This work was supported by the Air Force Office of Scientific Research [Grant FA95502010211].

Supplemental Material: The online appendix is available at https://doi.org/10.1287/opre.2023.2478.