Optimal Differentially Private Sampling of Unbounded Gaussians

Abstract

We provide the first $\widetilde{\mathcal{O}}\left(d\right)$-sample algorithm for sampling from unbounded Gaussian distributions under the constraint of $\left(\varepsilon, \delta\right)$-differential privacy. This is a quadratic improvement over previous results for the same problem, settling an open question of Ghazi, Hu, Kumar, and Manurangsi.