The Sample Complexity of Best-k Items Selection from Pairwise Comparisons

Jul 12, 2020



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, of which 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.


About ICML 2020

The International Conference on Machine Learning (ICML) is the premier gathering of professionals dedicated to the advancement of the branch of artificial intelligence known as machine learning. ICML is globally renowned for presenting and publishing cutting-edge research on all aspects of machine learning used in closely related areas like artificial intelligence, statistics and data science, as well as important application areas such as machine vision, computational biology, speech recognition, and robotics. ICML is one of the fastest growing artificial intelligence conferences in the world. Participants at ICML span a wide range of backgrounds, from academic and industrial researchers, to entrepreneurs and engineers, to graduate students and postdocs.

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