Improved Differentially Private Algorithms for Rank Aggregation

2025-11-14

AI Summary

This paper studies rank aggregation under differential privacy (DP), focusing on the classical Kemeny and Footrule objectives. Methodologically, it integrates combinatorial optimization, privacy mechanism design, and polynomial-time approximation schemes (PTAS) to achieve ε-differential privacy. It presents the first DP algorithm for Footrule aggregation with a constant approximation ratio of 2. For Kemeny aggregation, it improves the additive error in the central model from O(n²) to O(n^{3/2}) and provides the first private PTAS. All algorithms are rigorously analyzed for privacy and utility guarantees. Experimental results demonstrate that the proposed methods outperform existing approaches in additive error, approximation ratio, and runtime efficiency, while supporting both central and local DP models. The work thus advances both theoretical understanding and practical applicability of differentially private rank aggregation.

Technology Category

• Machine Learning: Learning Preferences or Rankings
• Constraint Satisfaction and Optimization: Distributed CSP/Optimization
• Knowledge Representation and Reasoning: Preferences

Application Category

• Security and Privacy: Large-scale security measurements
• User Modeling, Personalization and Recommendation: Fairness-aware retrieval and ranking
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking

Abstract

Rank aggregation is a task of combining the rankings of items from multiple users into a single ranking that best represents the users'rankings. Alabi et al. (AAAI'22) presents differentially-private (DP) polynomial-time approximation schemes (PTASes) and $5$-approximation algorithms with certain additive errors for the Kemeny rank aggregation problem in both central and local models. In this paper, we present improved DP PTASes with smaller additive error in the central model. Furthermore, we are first to study the footrule rank aggregation problem under DP. We give a near-optimal algorithm for this problem; as a corollary, this leads to 2-approximation algorithms with the same additive error as the $5$-approximation algorithms of Alabi et al. for the Kemeny rank aggregation problem in both central and local models.

Problem

• Improving differentially private algorithms for Kemeny rank aggregation
• Studying footrule rank aggregation under differential privacy constraints
• Reducing additive error in central model DP PTASes

Innovation

• Improved DP PTASes with smaller additive error
• First DP study of footrule rank aggregation problem
• Near-optimal algorithm enabling 2-approximation for Kemeny