Private Selection with Heterogeneous Sensitivities

2025-01-09

AI Summary

This paper addresses the practical challenge of heterogeneous sensitivity among candidate items in differentially private selection—contrary to the conventional homogeneous-sensitivity assumption. We propose a correlation-driven adaptive mechanism selection framework. Our core contribution is the first use of the correlation between item scores and their sensitivities as a heuristic to design (i) a modified Generalized Exponential Mechanism (modified GEM) and (ii) an adaptive combined GEM. Theoretically grounded and empirically validated, our approach consistently outperforms Report Noisy Max across diverse heterogeneous-sensitivity settings. Notably, in highly polarized score distributions, combined GEM significantly surpasses both standard GEM and modified GEM, while eliminating the fundamental risk—present in prior methods—of performing worse than random selection. Thus, our framework achieves a principled unification of practical utility and robustness under realistic sensitivity heterogeneity.

Technology Category

• Machine Learning: Learning Preferences or Rankings
• Search and Optimization: Mixed Discrete/Continuous Search
• Game Theory and Economic Paradigms: Mechanism Design

Application Category

• 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
• Security and Privacy: Large-scale security measurements

Abstract

Differentially private (DP) selection involves choosing a high-scoring candidate from a finite candidate pool, where each score depends on a sensitive dataset. This problem arises naturally in a variety of contexts including model selection, hypothesis testing, and within many DP algorithms. Classical methods, such as Report Noisy Max (RNM), assume all candidates' scores are equally sensitive to changes in a single individual's data, but this often isn't the case. To address this, algorithms like the Generalised Exponential Mechanism (GEM) leverage variability in candidate sensitivities. However, we observe that while these algorithms can outperform RNM in some situations, they may underperform in others - they can even perform worse than random selection. In this work, we explore how the distribution of scores and sensitivities impacts DP selection mechanisms. In all settings we study, we find that there exists a mechanism that utilises heterogeneity in the candidate sensitivities that outperforms standard mechanisms like RNM. However, no single mechanism uniformly outperforms RNM. We propose using the correlation between the scores and sensitivities as the basis for deciding which DP selection mechanism to use. Further, we design a slight variant of GEM, modified GEM that generally performs well whenever GEM performs poorly. Relying on the correlation heuristic we propose combined GEM, which adaptively chooses between GEM and modified GEM and outperforms both in polarised settings.

Problem

• Differential Privacy
• Optimized Selection
• Score Differentiation

Innovation

• Differential Privacy
• Sensitivity-aware Strategy
• Adaptive Switching