Nearly-Optimal Private Selection via Gaussian Mechanism

2025-11-10

AI Summary

This paper investigates the selection problem under differential privacy: whether the optimal error bound of the exponential mechanism can be approached using only adaptive calls to the Gaussian mechanism on low-sensitivity queries. The authors establish, for the first time, that relying solely on the Gaussian mechanism—without invoking the exponential mechanism or other complex primitives—and combining sensitivity analysis, adaptive query design, and optimized composition-theorem-based privacy budget allocation, achieves a selection error of $ ilde{O}(log |mathcal{Y}|)$. This improves upon the prior best bound of $O(log^{3/2} |mathcal{Y}|)$, nearly matching the theoretical lower bound. The result reveals the fundamental expressive power of the Gaussian mechanism for private selection tasks and establishes a new paradigm for designing lightweight, scalable differentially private algorithms.

Technology Category

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

Application Category

• Security and Privacy: Large-scale security measurements
• User Modeling, Personalization and Recommendation: User privacy protection in personalized systems
• Economics, Online Markets and Human Computation: Fairness, privacy, and diversity in economic environments

Abstract

Steinke (2025) recently asked the following intriguing open question: Can we solve the differentially private selection problem with nearly-optimal error by only (adaptively) invoking Gaussian mechanism on low-sensitivity queries? We resolve this question positively. In particular, for a candidate set $mathcal{Y}$, we achieve error guarantee of $ ilde{O}(log |mathcal{Y}|)$, which is within a factor of $(log log |mathcal{Y}|)^{O(1)}$ of the exponential mechanism (McSherry and Talwar, 2007). This improves on Steinke's mechanism which achieves an error of $O(log^{3/2} |mathcal{Y}|)$.

Problem

• Achieving near-optimal error in private selection
• Using only Gaussian mechanisms on low-sensitivity queries
• Improving error bounds over previous mechanisms

Innovation

• Uses Gaussian mechanism for private selection
• Achieves nearly-optimal error guarantee
• Improves upon previous logarithmic error bounds