Exactly Optimal and Communication-Efficient Private Estimation via Block Designs

TL;DR

This paper introduces a new class of local differential privacy schemes based on combinatorial block designs, achieving optimal privacy-utility trade-offs with low communication costs, and extends the framework to broader designs for wider applicability.

Contribution

It proposes a unified combinatorial block design framework for LDP schemes, discovering new schemes that are exactly optimal or near-optimal with minimal communication costs.

Findings

New LDP schemes achieve the optimal privacy-utility trade-off.

These schemes have the lowest communication costs among unbiased or consistent schemes.

Broader RPBD schemes extend applicability to more data sizes and privacy constraints.

Abstract

In this paper, we propose a new class of local differential privacy (LDP) schemes based on combinatorial block designs for discrete distribution estimation. This class not only recovers many known LDP schemes in a unified framework of combinatorial block design, but also suggests a novel way of finding new schemes achieving the exactly optimal (or near-optimal) privacy-utility trade-off with lower communication costs. Indeed, we find many new LDP schemes that achieve the exactly optimal privacy-utility trade-off, with the minimum communication cost among all the unbiased or consistent schemes, for a certain set of input data size and LDP constraint. Furthermore, to partially solve the sparse existence issue of block design schemes, we consider a broader class of LDP schemes based on regular and pairwise-balanced designs, called RPBD schemes, which relax one of the symmetry requirements on block designs. By considering this broader class of RPBD schemes, we can find LDP schemes achieving near-optimal privacy-utility trade-off with reasonably low communication costs for a much larger set of input data size and LDP constraint.