The Sample Complexity of Best-k Items Selection from Pairwise Comparisons
By Wenbo Ren, Jia Liu, Ness B. Shroff. 2020
18 citations recorded by the source corpus.
This paper studies the sample complexity (aka number of comparisons) bounds for the active best-$k$ items selection from pairwise comparisons. From a given set of items, the learner can make pairwise comparisons on every pair of items, and each comparison returns an independent noisy result about the preferred item. At any time, the learner can adaptively choose a pair of items to compare according to past observations (i.e., active learning). The learner's goal is to find the (approximately) best-$k$ items with a given confidence, while trying to use as few comparisons as possible. In this paper, we study two problems: (i) finding the probably approximately correct (PAC) best-$k$ items and (ii) finding the exact best-$k$ items, both under strong stochastic transitivity and stochastic triangle inequality. For PAC best-$k$ items selection, we first show a lower bound and then propose an algorithm whose sample complexity upper bound matches the lower bound up to a constant factor. For the exact best-$k$ items selection, we first prove a worst-instance lower bound. We then propose two algorithms based on our PAC best items selection algorithms: one works for $k=1$ and is sample complexity optimal up to a loglog factor, and the other works for all values of $k$ and is sample complexity optimal up to a log factor.
Subfields: Artificial Intelligence, Management Science and Operations Research, Statistical Learning Theory
How researchers see this paper
The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.
In Artificial Intelligence
- Nick Craswell
- Ellen M. Voorhees
- C. Clarke
- Xinyi Yan
- Cheng-hsin Luo
- Pablo Castells
- Jimmy J. Lin
- Bhaskar Mitra
In Management Science and Operations Research
- Nick Craswell
- Cheng-hsin Luo
- Ellen M. Voorhees
- C. Clarke
- Xinyi Yan
- Pablo Castells
- Bhaskar Mitra
- Jimmy J. Lin
Citations in the corpus
- Human Preferences as Dueling Bandits (2022, background): “For example, strategies that repeatedly compare two arms until a winner is found may require too many independent assessors to be feasible when arms are nearly equal [12, 13, 26].”