On the Interplay of Privacy, Persuasion and Quantization

摘要

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 ($X$,$θ$) and transmits a finite-rate message $Z$ to aid a legitimate controller (the decoder) in estimating $X+θ$, while an eavesdropper intercepts $Z$ to infer the private parameter $θ$. 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 $θ$. 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.