Nearly-Optimal Private Selection via Gaussian Mechanism

TL;DR

This paper presents a nearly-optimal differentially private selection method using Gaussian mechanisms, achieving error close to the exponential mechanism and improving upon previous approaches.

Contribution

It provides a positive solution to Steinke's open question by achieving near-optimal error with Gaussian mechanisms for private selection.

Findings

Achieves error of O(\u221a{ ext{log} |\u211d|}) for private selection.

Error is within a ( ext{log} ext{log} |\u211d|)^{O(1)} factor of the exponential mechanism.

Improves upon Steinke's previous mechanism with higher error bounds.

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 $\tilde{O}(\log |\mathcal{Y}|)$, 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 $O(\log^{3/2} |\mathcal{Y}|)$.