The Podium Mechanism: Improving on the Laplace and Staircase Mechanisms

Abstract: The Podium mechanism guarantees ($\epsilon, 0$)-differential privacy by sampling noise from a \emph{finite} mixture of three uniform distributions. By carefully constructing such a mixture distribution, we trivially guarantee privacy properties, while minimizing the variance of the noise added to our continuous outcome. Our gains in variance control are due to the "truncated" nature of the Podium mechanism where support for the noise distribution is maintained as close as possible to the sensitivity of our data collection, unlike the \emph{infinite} support that characterizes both the Laplace and Staircase mechanisms. In a high-privacy regime ($\epsilon < 1$), the Podium mechanism outperforms the other two by 50-70\% in terms of the noise variance reduction, while in a low privacy regime ($\epsilon \to \infty$), it asymptotically approaches the Staircase mechanism.