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Optimal Real-Time Fusion of Time-Series Data Under Rényi Differential Privacy

Chuanghong Weng, Ehsan Nekouei

TL;DR

This paper formulate the privacy-aware fusion design as a constrained finite-horizon optimization problem, in which the fusion policy and the state estimation are jointly optimized to minimize the state estimation error subject to a total privacy budget constraint.

Abstract

In this paper, we investigate the optimal real-time fusion of data collected by multiple sensors. In our set-up, the sensor measurements are considered to be private and are jointly correlated with an underlying process. A fusion center combines the private sensor measurements and releases its output to an honest-but-curious party, which is responsible for estimating the state of the underlying process based on the fusion center's output. The privacy leakage incurred by the fusion policy is quantified using Rényi differential privacy. We formulate the privacy-aware fusion design as a constrained finite-horizon optimization problem, in which the fusion policy and the state estimation are jointly optimized to minimize the state estimation error subject to a total privacy budget constraint. We derive the constrained optimality conditions for the proposed optimization problem and use them to characterize the structural properties of the optimal fusion policy. Unlike classical differential privacy mechanisms, the optimal fusion policy is shown to adaptively allocates the privacy budget and regulates the adversary's belief in a closed-loop manner. To reduce the computational burden of solving the resulting constrained optimality equations, we parameterize the fusion policy using a structured Gaussian distribution and show that the parameterized fusion policy satisfies the privacy constraint. We further develop a numerical algorithm to jointly optimize the fusion policy and state estimator. Finally, we demonstrate the effectiveness of the proposed fusion framework through a traffic density estimation case study.

Optimal Real-Time Fusion of Time-Series Data Under Rényi Differential Privacy

TL;DR

This paper formulate the privacy-aware fusion design as a constrained finite-horizon optimization problem, in which the fusion policy and the state estimation are jointly optimized to minimize the state estimation error subject to a total privacy budget constraint.

Abstract

In this paper, we investigate the optimal real-time fusion of data collected by multiple sensors. In our set-up, the sensor measurements are considered to be private and are jointly correlated with an underlying process. A fusion center combines the private sensor measurements and releases its output to an honest-but-curious party, which is responsible for estimating the state of the underlying process based on the fusion center's output. The privacy leakage incurred by the fusion policy is quantified using Rényi differential privacy. We formulate the privacy-aware fusion design as a constrained finite-horizon optimization problem, in which the fusion policy and the state estimation are jointly optimized to minimize the state estimation error subject to a total privacy budget constraint. We derive the constrained optimality conditions for the proposed optimization problem and use them to characterize the structural properties of the optimal fusion policy. Unlike classical differential privacy mechanisms, the optimal fusion policy is shown to adaptively allocates the privacy budget and regulates the adversary's belief in a closed-loop manner. To reduce the computational burden of solving the resulting constrained optimality equations, we parameterize the fusion policy using a structured Gaussian distribution and show that the parameterized fusion policy satisfies the privacy constraint. We further develop a numerical algorithm to jointly optimize the fusion policy and state estimator. Finally, we demonstrate the effectiveness of the proposed fusion framework through a traffic density estimation case study.
Paper Structure (26 sections, 4 theorems, 42 equations, 8 figures, 2 algorithms)

This paper contains 26 sections, 4 theorems, 42 equations, 8 figures, 2 algorithms.

Table of Contents

  1. Introduction
  2. Motivation
  3. Related Work
  4. Contributions
  5. Outline
  6. Notation
  7. Problem Formulation
  8. System Model
  9. Motivating Example
  10. Privacy-Aware Fusion and Estimation
  11. Privacy Measure
  12. Optimal Privacy-Aware Fusion Design
  13. Structural Properties of Optimal Privacy-Aware Fusion Design
  14. Constrained Optimality Equations
  15. Numerical Algorithm
  16. ...and 11 more sections

Key Result

Theorem 1

The optimal differential private fusion collection $\mathcal{C}$ can be obtained via solving the following constrained optimality equations, where $s_k$ is the remaining privacy budget with $s_k=s_{k-1}-L_{k-1}\left( \mathcal{C} _{k-1}\left( b_{k-1}, s_{k-1} \right) ;\alpha \right)$ and $s_1 = \mathsf{B_G}$, $b_k\left(X_k,Y_k\right)=p\left(X_k, Y^k \middle| Z^{k-1}\right)$ is the belief state wi

Figures (8)

  • Figure 1: Privacy-aware sensor fusion with adaptive budget allocation
  • Figure 2: Traffic density estimation through randomly reported position and speed measurements
  • Figure 3: Traffic density in US-101 Highway dataset
  • Figure 4: The structure of the optimal fusion policy.
  • Figure 5: The structure of the parameterized fusion policy.
  • ...and 3 more figures

Theorems & Definitions (7)

  • Theorem 1
  • proof
  • Lemma 1
  • Theorem 2
  • proof
  • Lemma 2
  • proof