On the Interplay of Privacy, Persuasion and Quantization

TL;DR

This paper introduces a communication-theoretic framework for privacy-aware decision making in cyber-physical systems, balancing control accuracy and privacy leakage against an eavesdropper, with analysis of optimal strategies and numerical results.

Contribution

It develops a novel framework combining privacy and control objectives, analyzing optimal encoding strategies under rate constraints and proposing gradient-based methods for finite-rate channels.

Findings

Optimal linear encoders characterized without rate constraints

Trade-off between control performance and privacy adjustable via privacy parameter

Gradient-based algorithms effectively compute optimal controllers under finite rates

Abstract

We develop a communication-theoretic framework for privacy-aware and resilient decision making in cyber-physical systems under misaligned objectives between the encoder and the decoder. The encoder observes two correlated signals ($X$,$\theta$) and transmits a finite-rate message $Z$ to aid a legitimate controller (the decoder) in estimating $X+\theta$, while an eavesdropper intercepts $Z$ to infer the private parameter $\theta$. Unlike conventional setups where encoder and decoder share a common MSE objective, here the encoder minimizes a Lagrangian that balances legitimate control fidelity and the privacy leakage about $\theta$. In contrast, the decoder's goal is purely to minimize its own estimation error without regard for privacy. We analyze fully, partially, and non-revealing strategies that arise from this conflict, and characterize optimal linear encoders when the rate constraints are lifted. For finite-rate channels, we employ gradient-based methods to compute the optimal controllers. Numerical experiments illustrate how tuning the privacy parameter shapes the trade-off between control performance and resilience against unauthorized inferences.