Bridging Central and Local Differential Privacy in Data Acquisition Mechanisms

34 Pages Posted: 27 Dec 2022 Last revised: 15 Mar 2023

See all articles by Alireza Fallah

Alireza Fallah

University of California, Berkeley

Ali Makhdoumi

Fuqua School of Business; Massachusetts Institute of Technology (MIT)

Azarakhsh Malekian

University of Toronto - Rotman School of Management; Massachusetts Institute of Technology (MIT) - Electrical Engineering and Computer Science

Asuman E. Ozdaglar

Massachusetts Institute of Technology (MIT) - Department of Electrical Engineering and Computer Science

Date Written: December 24, 2022

Abstract

We study the design of optimal Bayesian data acquisition mechanisms for a platform interested in estimating the mean of a distribution by collecting data from privacy-conscious users. In our setting, users have heterogeneous sensitivities for two types of privacy losses corresponding to local and central privacy measures. The local privacy loss of a user is due to the leakage of a user's information when she shares her data with the platform, and the central privacy loss of a user is due to the released estimate by the platform to the public. The users share their data in exchange for a payment (e.g., through monetary transfers or services) that compensates for their privacy losses. The platform does not know the privacy sensitivity of users and must design a mechanism to solicit their preferences and then deliver both local and central privacy guarantees while minimizing the estimation error plus the expected payment to users. We first establish minimax lower bounds for the estimation error, given a vector of privacy guarantees, and show that a linear estimator is (near) optimal. We then turn to our main goal: designing an optimal data acquisition mechanism. We establish that the design of such mechanisms in a Bayesian setting (where the platform knows the distribution of users' sensitivities and not their realizations) can be cast as a nonconvex optimization problem. Using a primal-dual argument, we prove that finding the optimal mechanism admits a Polynomial Time Approximation Scheme (PTAS).

Keywords: Differential privacy, Bayesian mechanism design, Minimax lower bound, Local and central differential privacy, Data markets

Suggested Citation

Fallah, Alireza and Makhdoumi, Ali and Malekian, Azarakhsh and Ozdaglar, Asuman E., Bridging Central and Local Differential Privacy in Data Acquisition Mechanisms (December 24, 2022). Rotman School of Management Working Paper No. 4311351, Available at SSRN: https://ssrn.com/abstract=4311351 or http://dx.doi.org/10.2139/ssrn.4311351

Alireza Fallah (Contact Author)

University of California, Berkeley ( email )

310 Barrows Hall
Berkeley, CA 94720
United States

Ali Makhdoumi

Fuqua School of Business ( email )

Box 90120
Durham, NC 27708-0120
United States

HOME PAGE: http://https://www.fuqua.duke.edu/faculty/ali-makhdoumi

Massachusetts Institute of Technology (MIT) ( email )

77 Massachusetts Avenue
50 Memorial Drive
Cambridge, MA 02139-4307
United States

Azarakhsh Malekian

University of Toronto - Rotman School of Management ( email )

105 St. George Street
Toronto, Ontario M5S 3E6 M5S1S4
Canada

Massachusetts Institute of Technology (MIT) - Electrical Engineering and Computer Science ( email )

77 Massachusetts Avenue
Cambridge, MA 02139-4307
United States

Asuman E. Ozdaglar

Massachusetts Institute of Technology (MIT) - Department of Electrical Engineering and Computer Science ( email )

50 Memorial Drive
Cambridge, MA 02139-4307
United States
617-324-0058 (Phone)

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