Universal Exact Compression of Differentially Private Mechanisms

TL;DR

This paper introduces Poisson private representation (PPR), a novel method for exactly compressing and simulating local differential privacy mechanisms, significantly reducing communication costs while preserving statistical properties.

Contribution

The paper presents PPR, a universal exact compression technique for local differential privacy mechanisms, achieving near-optimal size and maintaining all statistical properties.

Findings

PPR achieves compression within a logarithmic factor of the lower bound.

PPR provides a better communication-accuracy-privacy trade-off in distributed mean estimation.

Experimental results confirm PPR's superior performance over existing mechanisms.

Abstract

To reduce the communication cost of differential privacy mechanisms, we introduce a novel construction, called Poisson private representation (PPR), designed to compress and simulate any local randomizer while ensuring local differential privacy. Unlike previous simulation-based local differential privacy mechanisms, PPR exactly preserves the joint distribution of the data and the output of the original local randomizer. Hence, the PPR-compressed privacy mechanism retains all desirable statistical properties of the original privacy mechanism such as unbiasedness and Gaussianity. Moreover, PPR achieves a compression size within a logarithmic gap from the theoretical lower bound. Using the PPR, we give a new order-wise trade-off between communication, accuracy, central and local differential privacy for distributed mean estimation. Experiment results on distributed mean estimation show that PPR consistently gives a better trade-off between communication, accuracy and central differential privacy compared to the coordinate subsampled Gaussian mechanism, while also providing local differential privacy.