Differentially Private Parameter Estimation: Optimal Noise Insertion and Data Owner Selection

Xuanyu Cao, Tamer Basar

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Abstract

In this paper, we study differentially private parameter estimation in which a data acquisitor (DA) accesses data (or signals) from multiple privacy-aware data owners (DOs) to estimate some random parameters. To ensure differential privacy, the DOs add Laplace noises to their private signals and only reveal the noisy signals to the DA. Our goal is to add optimal amount of noises (measured by their variances) so that the mean squared error (MSE) of the DA's estimate is minimized while differential privacy is satisfied. In the general case, the optimal private estimation can be formulated as a semidefinite program (SDP), which can be readily solved by off-the-shelf optimization methods. In the special case where different DOs have uncorrelated signals, the optimization problem is decomposed across DOs and can be solved very efficiently in almost closed-form. We observe that, in the optimal solution, the DOs should add more noises to the signal entries that are less useful for estimation. Further, when the DA has DO selection constraint (e.g., due to limited budget), a relaxed SDP is put forth to compute a suboptimal solution. Finally, several numerical examples are presented.

Original languageEnglish (US)
Title of host publication2020 59th IEEE Conference on Decision and Control, CDC 2020
PublisherInstitute of Electrical and Electronics Engineers Inc.
Pages2887-2893
Number of pages7
ISBN (Electronic)9781728174471
DOIs
StatePublished - Dec 14 2020
Externally publishedYes
Event59th IEEE Conference on Decision and Control, CDC 2020 - Virtual, Jeju Island, Korea, Republic of
Duration: Dec 14 2020Dec 18 2020

Publication series

NameProceedings of the IEEE Conference on Decision and Control
Volume2020-December
ISSN (Print)0743-1546
ISSN (Electronic)2576-2370

Conference

Conference59th IEEE Conference on Decision and Control, CDC 2020
Country/TerritoryKorea, Republic of
CityVirtual, Jeju Island
Period12/14/2012/18/20

ASJC Scopus subject areas

  • Control and Systems Engineering
  • Modeling and Simulation
  • Control and Optimization

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