Differentially private iterative synchronous consensus

Huang, Zhengxu; Mitra, Sayan; Dullerud, Geir E.

doi:10.1145/2381966.2381978

Cited by 213 publications

(150 citation statements)

References 36 publications

(29 reference statements)

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“…The results in this paper generalize our previous work on differentially private iterative consensus [8] where the agent are required to converge to a common value while preserving the privacy of their initial values. Setting the coupling to zero, it is possible to recover the mechanism in [8] from the communication strategy proposed here.…”

Section: Related Work On Differential Privacysupporting

confidence: 66%

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On the cost of differential privacy in distributed control systems

Huang

Wang

Mitra

et al. 2014

Proceedings of the 3rd International Conference on High Confidence Networked Systems

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Individuals sharing information can improve the cost or performance of a distributed control system. But, sharing may also violate privacy. We develop a general framework for studying the cost of differential privacy in systems where a collection of agents, with coupled dynamics, communicate for sensing their shared environment while pursuing individual preferences. First, we propose a communication strategy that relies on adding carefully chosen random noise to agent states and show that it preserves differential privacy. Of course, the higher the standard deviation of the noise, the higher the cost of privacy. For linear distributed control systems with quadratic cost functions, the standard deviation becomes independent of the number agents and it decays with the maximum eigenvalue of the dynamics matrix. Furthermore, for stable dynamics, the noise to be added is independent of the number of agents as well as the time horizon up to which privacy is desired. Finally, we show that the cost of -differential privacy up to time T , for a linear stable system with N agents, is upper bounded by O( T 3 N 2 ).

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Section: Related Work On Differential Privacysupporting

confidence: 66%

“…Setting the coupling to zero, it is possible to recover the mechanism in [8] from the communication strategy proposed here.…”

Section: Related Work On Differential Privacymentioning

confidence: 99%

On the cost of differential privacy in distributed control systems

Huang

Wang

Mitra

et al. 2014

Proceedings of the 3rd International Conference on High Confidence Networked Systems

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“…Since its introduction in [2], the Laplacian mechanism has become the standard tool in differential privacy and has been used as the basic building block in a number of works on differential privacy analysis in other more complex problem settings, e.g., [10], [11], [12], [13], [14], [5], [15], [16], [17], [18], [19], [20], [21], [22], [23], [24], [25], [26], [27], [28], [29], [30], [31], [32], [33], [34], [35], [36], [37], [38], [39], [40], [41], [42], [43], [44], [45], [46]. Given this near-routine use of the query-output independent adding of Laplacian noise, the following two questions are natural:…”

Section: ) Laplacian Mechanismmentioning

confidence: 99%

The optimal mechanism in differential privacy

Geng¹,

Viswanath²

2014

2014 IEEE International Symposium on Information Theory

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Differential privacy is a framework to quantify to what extent individual privacy in a statistical database is preserved while releasing useful aggregate information about the database. In this work we study the fundamental tradeoff between privacy and utility in differential privacy. We derive the optimal -differentially private mechanism for single real-valued query function under a very general utility-maximization (or cost-minimization) framework. The class of noise probability distributions in the optimal mechanism has staircase-shaped probability density functions which are symmetric (around the origin), monotonically decreasing and geometrically decaying. The staircase mechanism can be viewed as a geometric mixture of uniform probability distributions, providing a simple algorithmic description for the mechanism. Furthermore, the staircase mechanism naturally generalizes to discrete query output settings as well as more abstract settings. We explicitly derive the parameter of the optimal staircase mechanism for 1 and 2 cost functions. Comparing the optimal performances with those of the usual Laplacian mechanism, we show that in the high privacy regime ( is small), the Laplacian mechanism is asymptotically optimal as → 0; in the low privacy regime ( is large), the minimum magnitude and second moment of noise are Θ(∆e3 ) as → +∞, respectively, while the corresponding figures when using the Laplacian mechanism are ∆ and, where ∆ is the sensitivity of the query function. We conclude that the gains of the staircase mechanism are more pronounced in the moderate-low privacy regime.

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“…In [3], the notion of differential privacy was extended to dynamical systems to preserve the privacy of the inputs. Iterative consensus seeking algorithms that preserve the privacy of the initial conditions of the participants were considered in [4]. Corrupting the state measurements of agents in a distributed control setup was explored in [5] to keep the preferences of the agents (i.e., the way points that need to be followed) private.…”

Section: Introductionmentioning

confidence: 99%

Optimal state estimation with measurements corrupted by Laplace noise

Farokhi

Milošević

2016

2016 IEEE 55th Conference on Decision and Control (CDC)

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Abstract-Optimal state estimation for linear discrete-time systems is considered. Motivated by the literature on differential privacy, the measurements are assumed to be corrupted by Laplace noise. The optimal least mean square error estimate of the state is approximated using a randomized method. The method relies on that the Laplace noise can be rewritten as Gaussian noise scaled by Rayleigh random variable. The probability of the event that the distance between the approximation and the best estimate is smaller than a constant is determined as function of the number of parallel Kalman filters that is used in the randomized method. This estimator is then compared with the optimal linear estimator, the maximum a posteriori (MAP) estimate of the state, and the particle filter.

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Differentially private iterative synchronous consensus

Cited by 213 publications

References 36 publications

On the cost of differential privacy in distributed control systems

On the cost of differential privacy in distributed control systems

The optimal mechanism in differential privacy

Optimal state estimation with measurements corrupted by Laplace noise

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