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arXiv:2506.06321 · IEEE Conference on Decision and Control (CDC)

On the Interplay of Privacy, Persuasion, and Quantization

Anju Anand, Emrah Akyol

Published Dec 9, 2025• 1 citation
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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,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 mean squared error objective, here the encoder minimizes a Lagrangian that balances legitimate control fidelity and the information 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.

DOI
10.1109/cdc57313.2025.11312389

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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 mean squared error objective, here the encoder minimizes a Lagrangian that balances legitimate control fidelity and the information 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.
We consider a privacy-signaling game problem in which a transmitter with privacy concerns and a receiver, which does not pay attention to these privacy concerns, communicate. In this communication scenario, the transmitter observes a pair of correlated random variables which are modeled as jointly Gaussian. The transmitter constructs its message based on these random variables with the aim to hide one of them and convey the other one. In contrast, the objective of the receiver is to accurately estimate both of the random variables so as to gather as much information as possible. These conflicting objectives are analyzed in a game theoretic framework where depending on the commitment conditions (of the sender), we consider Nash or Stackelberg equilibria. We show that a payoff dominant (i.e., most desirable for both players) Nash equilibrium is attained by affine policies and we explicitly characterize these policies. In addition, the strategies at the characterized Nash equilibrium is shown to form also a Stackelberg equilibrium. Furthermore, we show that there always exists an informative Stackelberg equilibrium for the multidimensional parameter setup. We also revisit the information bottleneck problem within our Stackelberg framework under the mean squared error distortion criterion where the information bottleneck setup has a further restriction that only one of the parameters is observed at the sender. We fully characterize the Stackelberg equilibria under certain conditions and when these conditions are not met we establish the existence of informative equilibria.
We introduce a privacy-signaling game problem in which a transmitter with privacy concerns observes a pair of correlated random vectors which are modeled as jointly Gaussian. The transmitter aims to hide one of these random vectors and convey the other one whereas the objective of the receiver is to accurately estimate both of the random vectors. We analyze these conflicting objectives in a game theoretic framework where depending on the commitment conditions (of the sender), we consider Nash or Stackelberg (Bayesian persuasion) equilibria. We show that a payoff dominant Nash equilibrium among all admissible policies is attained by a set of explicitly characterized linear policies. We also show that a payoff dominant Nash equilibrium coincides with a Stackelberg equilibrium. We formulate the information bottleneck problem within our Stackelberg framework under the mean squared error distortion criterion where the information bottleneck setup has a further restriction that only one of the parameters is observed at the sender. We show that this MMSE Gaussian Information Bottleneck Problem admits a linear solution which is explicitly characterized in the paper. We provide explicit conditions on when the optimal solutions, or equilibrium solutions in the Nash setup, are informative or noninformative.
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In this paper, optimal deterministic encoding of a vector parameter is investigated in the presence of an eavesdropper. The objective is to minimize the expectation of the conditional Cramér-Rao bound at the intended receiver, while satisfying an individual secrecy constraint on the mean-squared error of estimating each parameter at the eavesdropper. The eavesdropper is modeled to employ the linear minimum mean-squared error estimator based on the noisy observation of the encoded parameter without being aware of encoding. First, the problem is formulated as a constrained optimization problem in the space of vector-valued functions. Then, two practical solution strategies are developed based on nonlinear individual encoding and affine joint encoding of parameters. Theoretical results on the solutions of the proposed strategies are provided for various scenarios on channel conditions and parameter distributions. Finally, numerical examples are presented to illustrate the performance of the proposed solution approaches.
We investigate a privacy-signaling game problem in which a sender with privacy concerns observes a pair of correlated random vectors which are modeled as jointly Gaussian. The sender aims to hide one of these random vectors and convey the other one whereas the objective of the receiver is to accurately estimate both of the random vectors. We analyze these conflicting objectives in a game theoretic framework with quadratic costs where depending on the commitment conditions (of the sender), we consider Nash or Stackelberg (Bayesian persuasion) equilibria. We show that a payoff dominant Nash equilibrium among all admissible policies is attained by a set of explicitly characterized linear policies. We also show that a payoff dominant Nash equilibrium coincides with a Stackelberg equilibrium. We formulate the information bottleneck problem within our Stackelberg framework under the mean squared error distortion criterion where the information bottleneck setup has a further restriction that only one of the random variables is observed at the sender. We show that this MMSE Gaussian Information Bottleneck Problem admits a linear solution which is explicitly characterized in the paper. We provide explicit conditions on when the optimal solutions, or equilibrium solutions in the Nash setup, are informative or noninformative.
In this manuscript, the problem of function computation with privacy constraints is considered. The problem consists of two legitimate nodes Alice and Bob, and an eavesdropper Eve. Bob would like to compute a function, and the arguments of the function are two source observation sequences that are distributed over the legitimate nodes respectively. To make the function computable at Bob, Alice is allowed to transmit a message to Bob via a public noiseless channel, which Eve has full access to. Under this model, we study the relationship among message rate, private information leakage to Bob and equivocation of Alice's source observations at Eve, and fully single-letter characterize the region of these achievable parameter tuples.