Minimum Weighted Feedback Arc Sets for Ranking from Pairwise Comparisons

TL;DR

This paper explores the connection between the Minimum Weighted Feedback Arc Set problem and ranking from pairwise comparisons, proposing combinatorial algorithms that outperform learning-based methods in speed and accuracy.

Contribution

It introduces efficient combinatorial algorithms for MWFAS that serve as a scalable, learning-free approach to ranking, challenging the dominance of deep learning methods.

Findings

Combinatorial algorithms run faster than learning-based methods.

These algorithms achieve comparable or better ranking accuracy.

Lightweight methods are effective for large-scale ranking tasks.

Abstract

The Minimum Weighted Feedback Arc Set (MWFAS) problem is closely related to the task of deriving a global ranking from pairwise comparisons. Recent work by He et al. (ICML 2022) advanced the state of the art on ranking benchmarks using learning based methods, but did not examine the underlying connection to MWFAS. In this paper, we investigate this relationship and introduce efficient combinatorial algorithms for solving MWFAS as a means of addressing the ranking problem. Our experimental results show that these simple, learning free methods achieve substantially faster runtimes than recent learning based approaches, while also delivering competitive, and in many cases superior, ranking accuracy. These findings suggest that lightweight combinatorial techniques offer a scalable and effective alternative to deep learning for large scale ranking tasks.