Nested Elimination: A Simple Algorithm for Best-Item Identification From Choice-Based Feedback

Junwen Yang, Yifan Feng
Proceedings of the 40th International Conference on Machine Learning, PMLR 202:39205-39233, 2023.

Abstract

We study the problem of best-item identification from choice-based feedback. In this problem, a company sequentially and adaptively shows display sets to a population of customers and collects their choices. The objective is to identify the most preferred item with the least number of samples and at a high confidence level. We propose an elimination-based algorithm, namely Nested Elimination (NE), which is inspired by the nested structure implied by the information-theoretic lower bound. NE is simple in structure, easy to implement, and has a strong theoretical guarantee for sample complexity. Specifically, NE utilizes an innovative elimination criterion and circumvents the need to solve any complex combinatorial optimization problem. We provide an instance-specific and non-asymptotic bound on the expected sample complexity of NE. We also show NE achieves high-order worst-case asymptotic optimality. Finally, numerical experiments from both synthetic and real data corroborate our theoretical findings.

Cite this Paper

BibTeX
@InProceedings{pmlr-v202-yang23b, title = {Nested Elimination: A Simple Algorithm for Best-Item Identification From Choice-Based Feedback}, author = {Yang, Junwen and Feng, Yifan}, booktitle = {Proceedings of the 40th International Conference on Machine Learning}, pages = {39205--39233}, year = {2023}, editor = {Krause, Andreas and Brunskill, Emma and Cho, Kyunghyun and Engelhardt, Barbara and Sabato, Sivan and Scarlett, Jonathan}, volume = {202}, series = {Proceedings of Machine Learning Research}, month = {23--29 Jul}, publisher = {PMLR}, pdf = {https://proceedings.mlr.press/v202/yang23b/yang23b.pdf}, url = {https://proceedings.mlr.press/v202/yang23b.html}, abstract = {We study the problem of best-item identification from choice-based feedback. In this problem, a company sequentially and adaptively shows display sets to a population of customers and collects their choices. The objective is to identify the most preferred item with the least number of samples and at a high confidence level. We propose an elimination-based algorithm, namely Nested Elimination (NE), which is inspired by the nested structure implied by the information-theoretic lower bound. NE is simple in structure, easy to implement, and has a strong theoretical guarantee for sample complexity. Specifically, NE utilizes an innovative elimination criterion and circumvents the need to solve any complex combinatorial optimization problem. We provide an instance-specific and non-asymptotic bound on the expected sample complexity of NE. We also show NE achieves high-order worst-case asymptotic optimality. Finally, numerical experiments from both synthetic and real data corroborate our theoretical findings.} }
Endnote
%0 Conference Paper %T Nested Elimination: A Simple Algorithm for Best-Item Identification From Choice-Based Feedback %A Junwen Yang %A Yifan Feng %B Proceedings of the 40th International Conference on Machine Learning %C Proceedings of Machine Learning Research %D 2023 %E Andreas Krause %E Emma Brunskill %E Kyunghyun Cho %E Barbara Engelhardt %E Sivan Sabato %E Jonathan Scarlett %F pmlr-v202-yang23b %I PMLR %P 39205--39233 %U https://proceedings.mlr.press/v202/yang23b.html %V 202 %X We study the problem of best-item identification from choice-based feedback. In this problem, a company sequentially and adaptively shows display sets to a population of customers and collects their choices. The objective is to identify the most preferred item with the least number of samples and at a high confidence level. We propose an elimination-based algorithm, namely Nested Elimination (NE), which is inspired by the nested structure implied by the information-theoretic lower bound. NE is simple in structure, easy to implement, and has a strong theoretical guarantee for sample complexity. Specifically, NE utilizes an innovative elimination criterion and circumvents the need to solve any complex combinatorial optimization problem. We provide an instance-specific and non-asymptotic bound on the expected sample complexity of NE. We also show NE achieves high-order worst-case asymptotic optimality. Finally, numerical experiments from both synthetic and real data corroborate our theoretical findings.
APA
Yang, J. & Feng, Y.. (2023). Nested Elimination: A Simple Algorithm for Best-Item Identification From Choice-Based Feedback. Proceedings of the 40th International Conference on Machine Learning, in Proceedings of Machine Learning Research 202:39205-39233 Available from https://proceedings.mlr.press/v202/yang23b.html.

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