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

• URL: http://arxiv.org/abs/2307.09295v1
• Date: Thu, 13 Jul 2023 05:05:30 GMT
• Title: Nested Elimination: A Simple Algorithm for Best-Item Identification from Choice-Based Feedback
• Authors: Junwen Yang, Yifan Feng
• Abstract summary: 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. We propose an elimination-based algorithm, namely Nested Elimination (NE), which is inspired by the nested structure implied by the information-theoretic lower bound.
• Score: 8.043586007062858
• License: http://creativecommons.org/licenses/by-nc-nd/4.0/
• 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.

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