Stochastic Iterative Methods for Online Rank Aggregation from Pairwise Comparisons

TL;DR

This paper proposes stochastic gradient descent methods for large-scale online rank aggregation from pairwise comparisons, providing convergence guarantees and analyzing performance under noise and partial observations.

Contribution

It introduces novel stochastic iterative algorithms for rank aggregation, with theoretical convergence proofs and practical insights into noise tolerance and observation requirements.

Findings

Algorithms converge almost surely under various observation regimes.

Noise in comparisons can be tolerated up to a certain level.

Empirical results inform the number of observations needed for reliable ranking.

Abstract

In this paper, we consider large-scale ranking problems where one is given a set of (possibly non-redundant) pairwise comparisons and the underlying ranking explained by those comparisons is desired. We show that stochastic gradient descent approaches can be leveraged to offer convergence to a solution that reveals the underlying ranking while requiring low-memory operations. We introduce several variations of this approach that offer a tradeoff in speed and convergence when the pairwise comparisons are noisy (i.e., some comparisons do not respect the underlying ranking). We prove theoretical results for convergence almost surely and study several regimes including those with full observations, partial observations, and noisy observations. Our empirical results give insights into the number of observations required as well as how much noise in those measurements can be tolerated.