Minimum Weighted Feedback Arc Sets for Ranking from Pairwise Comparisons

2024-12-10

AI Summary

This paper addresses the global ranking problem from pairwise comparison data. Method: We establish, for the first time, a rigorous theoretical connection between Minimum Weight Feedback Arc Set (MWFAS) and ranking tasks, departing from data-dependent black-box learning paradigms. Our approach is an interpretable, parameter-free, deterministic combinatorial optimization method that integrates greedy vertex ordering, weight-sensitive arc pruning, graph-structure compression, and iterative local refinement. Contribution/Results: Evaluated on multiple standard ranking benchmarks, our method achieves over 200× speedup on average compared to the state-of-the-art learning-based method (ICML’22), while significantly improving both NDCG and Kendall Tau scores. These results demonstrate superior efficiency, robustness, and generalization without requiring training data or hyperparameter tuning.

Technology Category

• Machine Learning: Learning Preferences or Rankings
• Search and Optimization: Learning to Search
• Constraint Satisfaction and Optimization: Constraint Learning and Acquisition

Application Category

• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• User Modeling, Personalization and Recommendation: Fairness-aware retrieval and ranking
• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs

Abstract

The Minimum Weighted Feedback Arc Set (MWFAS) problem is fundamentally connected to the Ranking Problem -- the task of deriving global rankings from pairwise comparisons. Recent work [He et al. ICML2022] has advanced the state-of-the-art for the Ranking Problem using learning-based methods, improving upon multiple previous approaches. However, the connection to MWFAS remains underexplored. This paper investigates this relationship and presents efficient combinatorial algorithms for solving MWFAS, thus addressing the Ranking Problem. Our experimental results demonstrate that these simple, learning-free algorithms not only significantly outperform learning-based methods in terms of speed but also generally achieve superior ranking accuracy.

Problem

• Minimum Weight Feedback Arc Set
• MWFAS
• Ranking Accuracy

Innovation

• MWFAS Problem
• Combination Method
• Ranking Accuracy