Differentially private average consensus: Obstructions, trade-offs, and optimal algorithm design

Nozari, Erfan and Tallapragada, Pavankumar and Cortes, Jorge (2017) Differentially private average consensus: Obstructions, trade-offs, and optimal algorithm design. In: AUTOMATICA, 81 . pp. 221-231.

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Abstract

privacy of the agents' initial states against an adversary that has access to all the messages. We first establish that a differentially private consensus algorithm cannot guarantee convergence of the agents' states to the exact average in distribution, which in turn implies the same impossibility for other stronger notions of convergence. This result motivates our design of a novel differentially private Laplacian consensus algorithm in which agents linearly perturb their state-transitionand message-generating functions with exponentially decaying Laplace noise. We prove that our algorithm converges almost surely to an unbiased estimate of the average of agents' initial states, compute the exponential mean square rate of convergence, and formally characterize its differential privacy properties. We show that the optimal choice of our design parameters (with respect to the variance of the convergence point around the exact average) corresponds to a one-shot perturbation of initial states and compare our design with various counterparts from the literature. Simulations illustrate our results. (C)2017 Elsevier Ltd. All rights reserved.

Item Type:	Journal Article
Publication:	AUTOMATICA
Additional Information:	Copy right for this article belongs to the PERGAMON-ELSEVIER SCIENCE LTD, THE BOULEVARD, LANGFORD LANE, KIDLINGTON, OXFORD OX5 1GB, ENGLAND
Department/Centre:	Division of Electrical Sciences > Electrical Engineering
Date Deposited:	14 Jul 2017 04:52
Last Modified:	14 Jul 2017 04:52
URI:	http://eprints.iisc.ac.in/id/eprint/57370

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