The Podium Mechanism: Improving on the Laplace and Staircase Mechanisms.

The Podium mechanism guarantees ($epsilon, 0$)-differential privacy by sampling noise from a 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 our continuous outcome. Our gains in variance control are due the truncated nature of the Podium mechanism where support for the noise distribution is maintained as close as possible the sensitivity of our data collection, unlike the infinite support that characterizes both the Laplace and Staircase mechanisms. In a high-privacy regime ($epsilon u003c 1$), 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.