Nested Elimination: A Simple Algorithm for Best-Item Identification from
  Choice-Based Feedback
Junwen Yang Yifan Feng
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.