Randomized Kaczmarz for Rank Aggregation from Pairwise Comparisons

TL;DR

This paper introduces a randomized Kaczmarz algorithm for rank aggregation from pairwise comparisons under the BTL model, demonstrating theoretical convergence and empirical effectiveness in inferring overall rankings efficiently.

Contribution

The paper presents a novel application of the randomized Kaczmarz method to rank aggregation, with convergence analysis and practical algorithms for online and distributed settings.

Findings

Algorithm converges reliably under noisy data

Empirical results validate theoretical convergence rates

Method performs well in online and distributed environments

Abstract

We revisit the problem of inferring the overall ranking among entities in the framework of Bradley-Terry-Luce (BTL) model, based on available empirical data on pairwise preferences. By a simple transformation, we can cast the problem as that of solving a noisy linear system, for which a ready algorithm is available in the form of the randomized Kaczmarz method. This scheme is provably convergent, has excellent empirical performance, and is amenable to on-line, distributed and asynchronous variants. Convergence, convergence rate, and error analysis of the proposed algorithm are presented and several numerical experiments are conducted whose results validate our theoretical findings.