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arXiv · 2405.20782

Universal Exact Compression of Differentially Private Mechanisms

Yanxiao Liu·Wei-Ning Chen·Ayfer Özgür·Cheuk Ting Li
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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.

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Yanxiao Liu, Wei-Ning Chen, Ayfer Özgür, Cheuk Ting Li. 2024-11-10. Universal Exact Compression of Differentially Private Mechanisms. https://arxiv.org/abs/2405.20782

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