Optimal Compression of Locally Differentially Private Mechanisms

• URL: http://arxiv.org/abs/2111.00092v1
• Date: Fri, 29 Oct 2021 21:36:34 GMT
• Title: Optimal Compression of Locally Differentially Private Mechanisms
• Authors: Abhin Shah, Wei-Ning Chen, Johannes Balle, Peter Kairouz, Lucas Theis
• Abstract summary: We demonstrate the benefits of schemes that jointly compress and privatize the data using shared randomness. Our theoretical and empirical findings show that our approach can compress PrivUnit (Bhowmick et al., Coding and Subset Selection (Ye et al., the best known LDP algorithms for mean and frequency estimation, to the order of epsilon-bits of communication, while preserving their privacy and accuracy guarantees, to the order of epsilon-bits of communication, to the order of epsilon-bits of communication, to the order of epsilon-bits of communication, to the
• Score: 21.200464908282594
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Compressing the output of \epsilon-locally differentially private (LDP) randomizers naively leads to suboptimal utility. In this work, we demonstrate the benefits of using schemes that jointly compress and privatize the data using shared randomness. In particular, we investigate a family of schemes based on Minimal Random Coding (Havasi et al., 2019) and prove that they offer optimal privacy-accuracy-communication tradeoffs. Our theoretical and empirical findings show that our approach can compress PrivUnit (Bhowmick et al., 2018) and Subset Selection (Ye et al., 2018), the best known LDP algorithms for mean and frequency estimation, to to the order of \epsilon-bits of communication while preserving their privacy and accuracy guarantees.

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