Optimal Compression of Locally Differentially Private Mechanisms

TL;DR

This paper introduces a joint compression and privatization scheme for locally differentially private mechanisms, achieving optimal tradeoffs and significant communication reduction while maintaining privacy and accuracy.

Contribution

It proposes a novel approach based on Minimal Random Coding that optimally balances privacy, accuracy, and communication in LDP mechanisms.

Findings

Achieves near  bits of communication for LDP algorithms.

Proves optimal privacy-accuracy-communication tradeoffs.

Demonstrates empirical improvements over existing methods.

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.