Oneshot Differentially Private Top-k Selection

Abstract: Being able to efficiently and accurately select the top-$k$ elements with differential privacy is an integral component of various private data analysis tasks. In this paper, we present the oneshot Laplace mechanism, which generalizes the well-known Report Noisy Max mechanism to reporting noisy top-$k$ elements. We show that the oneshot Laplace mechanism with a noise level of $\widetilde{O}(\sqrt{k}/\eps)$ is approximately differentially private. Compared to the previous peeling approach of running Report Noisy Max $k$ times, the oneshot Laplace mechanism only adds noises and computes the top $k$ elements once, hence much more efficient for large $k$. In addition, our proof of privacy relies on a novel coupling technique that bypasses the use of composition theorems. Finally, we present a novel application of efficient top-$k$ selection in the classical problem of ranking from pairwise comparisons.