Inductive Pairwise Ranking: Going Beyond the n log(n) Barrier

TL;DR

This paper introduces the Inductive Pairwise Ranking (IPR) algorithm, which leverages feature information and matrix completion techniques to efficiently learn accurate rankings from limited pairwise preference data, surpassing traditional methods.

Contribution

The paper proposes a broad FLR model encompassing several existing preference models and develops the IPR algorithm with provable sample efficiency for ranking tasks.

Findings

IPR outperforms existing methods in sample complexity.

Effective ranking recovery with as low as 10% pairwise comparison sampling.

Theoretical validation of sample efficiency improvements.

Abstract

We study the problem of ranking a set of items from nonactively chosen pairwise preferences where each item has feature information with it. We propose and characterize a very broad class of preference matrices giving rise to the Feature Low Rank (FLR) model, which subsumes several models ranging from the classic Bradley-Terry-Luce (BTL) (Bradley and Terry 1952) and Thurstone (Thurstone 1927) models to the recently proposed blade-chest (Chen and Joachims 2016) and generic low-rank preference (Rajkumar and Agarwal 2016) models. We use the technique of matrix completion in the presence of side information to develop the Inductive Pairwise Ranking (IPR) algorithm that provably learns a good ranking under the FLR model, in a sample-efficient manner. In practice, through systematic synthetic simulations, we confirm our theoretical findings regarding improvements in the sample complexity due to the use of feature information. Moreover, on popular real-world preference learning datasets, with as less as 10% sampling of the pairwise comparisons, our method recovers a good ranking.