Differential Privacy in Linear Distributed Control Systems: Entropy Minimizing Mechanisms and Performance Tradeoffs

In distributed control systems with shared resources, participating agents can improve the overall performance of the system by sharing data about their personal preferences. In this paper, we formulate and study a natural tradeoff arising in these problems between the privacy of the agent's da...

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Bibliographic Details
Published in:IEEE transactions on control of network systems Vol. 4; no. 1; pp. 118 - 130
Main Authors: Yu Wang, Zhenqi Huang, Mitra, Sayan, Dullerud, Geir E.
Format: Journal Article
Language:English
Published: Piscataway IEEE 01.03.2017
The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subjects:
Communication networks
Control systems
Data privacy
Decentralized control
decision/estimation theory
differential privacy
Discrete time systems
distributed algorithms/control
Distributed control systems
Distributed databases
Entropy
Error analysis
Estimation
Lower bounds
Noise control
Noise sensitivity
Parameter sensitivity
Performance enhancement
Preferences
Privacy
Time measurement
Tracking errors
Tradeoffs
ISSN:2325-5870, 2372-2533
Online Access:Get full text
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Summary:In distributed control systems with shared resources, participating agents can improve the overall performance of the system by sharing data about their personal preferences. In this paper, we formulate and study a natural tradeoff arising in these problems between the privacy of the agent's data and the performance of the control system. We formalize privacy in terms of differential privacy of agents' preference vectors. The overall control system consists of N agents with linear discrete-time coupled dynamics, each controlled to track its preference vector. Performance of the system is measured by the mean squared tracking error. We present a mechanism that achieves differential privacy by adding Laplace noise to the shared information in a way that depends on the sensitivity of the control system to the private data. We show that for stable systems the performance cost of using this type of privacy preserving mechanism grows as O(T 3 /Nε 2 ), where T is the time horizon and ε is the privacy parameter. For unstable systems, the cost grows exponentially with time. From an estimation point of view, we establish a lower-bound for the entropy of any unbiased estimator of the private data from any noise-adding mechanism that gives ε-differential privacy. We show that the mechanism achieving this lower-bound is a randomized mechanism that also uses Laplace noise.
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ISSN:2325-5870
2372-2533
DOI:10.1109/TCNS.2017.2658190