Design of Stochastic Quantizers for Privacy Preservation

TL;DR

This paper explores how stochastic quantizers can be designed to balance privacy preservation and control performance, demonstrating that larger quantization steps can ensure differential privacy while analyzing trade-offs and proposing dynamic quantizers for improved privacy.

Contribution

It introduces a novel analysis of static and dynamic stochastic quantizers for privacy, establishing differential privacy guarantees and proposing methods to enhance privacy without sacrificing control quality.

Findings

Large quantization steps guarantee differential privacy.

Dynamic stochastic quantizers improve privacy over static ones.

Input Gaussian noise helps stabilize privacy in unstable systems.

Abstract

In this paper, we examine the role of stochastic quantizers for privacy preservation. We first employ a static stochastic quantizer and investigate its corresponding privacy-preserving properties. Specifically, we demonstrate that a sufficiently large quantization step guarantees $(0, \delta)$ differential privacy. Additionally, the degradation of control performance caused by quantization is evaluated as the tracking error of output regulation. These two analyses characterize the trade-off between privacy and control performance, determined by the quantization step. This insight enables us to use quantization intentionally as a means to achieve the seemingly conflicting two goals of maintaining control performance and preserving privacy at the same time; towards this end, we further investigate a dynamic stochastic quantizer. Under a stability assumption, the dynamic stochastic quantizer can enhance privacy, more than the static one, while achieving the same control performance. We further handle the unstable case by additionally applying input Gaussian noise.