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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Vydané v:	IEEE transactions on control of network systems Ročník 4; číslo 1; s. 118 - 130
Hlavní autori:	Yu Wang, Zhenqi Huang, Mitra, Sayan, Dullerud, Geir E.
Médium:	Journal Article
Jazyk:	English
Vydavateľské údaje:	Piscataway IEEE 01.03.2017 The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Predmet:	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
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Abstract	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.
AbstractList	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 [Formula Omitted] 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 [Formula Omitted], where [Formula Omitted] is the time horizon and [Formula Omitted] 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 [Formula Omitted]-differential privacy. We show that the mechanism achieving this lower-bound is a randomized mechanism that also uses Laplace noise. 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.
Author	Yu Wang Zhenqi Huang Mitra, Sayan Dullerud, Geir E.
Author_xml	– sequence: 1 surname: Yu Wang fullname: Yu Wang email: yuwang8@illinois.edu organization: Coordinate Sci. Lab., Univ. of Illinois at Urbana-Champaign, Urbana, IL, USA – sequence: 2 surname: Zhenqi Huang fullname: Zhenqi Huang email: zhuang25@illinois.edu organization: Coordinate Sci. Lab., Univ. of Illinois at Urbana-Champaign, Urbana, IL, USA – sequence: 3 givenname: Sayan surname: Mitra fullname: Mitra, Sayan email: mitras@illinois.edu organization: Coordinate Sci. Lab., Univ. of Illinois at Urbana-Champaign, Urbana, IL, USA – sequence: 4 givenname: Geir E. surname: Dullerud fullname: Dullerud, Geir E. email: dullerud@uiuc.edu organization: Coordinate Sci. Lab., Univ. of Illinois at Urbana-Champaign, Urbana, IL, USA
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SubjectTerms	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
Title	Differential Privacy in Linear Distributed Control Systems: Entropy Minimizing Mechanisms and Performance Tradeoffs
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