Optimal Compression of Locally Differentially Private Mechanisms
This work addresses communication efficiency in privacy-preserving data analysis, offering incremental improvements for applications like federated learning and secure data aggregation.
The paper tackles the problem of suboptimal utility when compressing locally differentially private mechanisms by introducing schemes that jointly compress and privatize data using shared randomness, achieving optimal privacy-accuracy-communication tradeoffs and compressing best-known LDP algorithms to ε-bits of communication while preserving guarantees.
Compressing the output of ε-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 ε-bits of communication while preserving their privacy and accuracy guarantees.