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Bridging Central and Local Differential Privacy in Data Acquisition Mechanisms
Alireza Fallah · Ali Makhdoumi · azarakhsh malekian · Asuman Ozdaglar

Thu Dec 01 02:00 PM -- 04:00 PM (PST) @ Hall J #813

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 differential privacy measures. The local privacy loss is due to the leakage of a user's information when she shares her data with the platform, and the central privacy loss 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. Additionally, for the class of linear estimators, we prove that finding the optimal mechanism admits a Polynomial Time Approximation Scheme.

Author Information

Alireza Fallah (MIT)
Ali Makhdoumi (Duke University)

Ali Makhdoumi is an Associate Professor in the Decision Sciences area at Fuqua School of Business, Duke University. He has received a BSc in Electrical Engineering and a BSc in Mathematics from the Sharif University of Technology and a Ph.D. in Electrical Engineering and Computer Science from MIT. His current research interests include data markets, privacy, algorithmic game theory, and networks.

azarakhsh malekian (University of Toronto)
Asuman Ozdaglar (Massachusetts Institute of Technology)

Asu Ozdaglar received the B.S. degree in electrical engineering from the Middle East Technical University, Ankara, Turkey, in 1996, and the S.M. and the Ph.D. degrees in electrical engineering and computer science from the Massachusetts Institute of Technology, Cambridge, in 1998 and 2003, respectively. She is currently a professor in the Electrical Engineering and Computer Science Department at the Massachusetts Institute of Technology. She is also the director of the Laboratory for Information and Decision Systems. Her research expertise includes optimization theory, with emphasis on nonlinear programming and convex analysis, game theory, with applications in communication, social, and economic networks, distributed optimization and control, and network analysis with special emphasis on contagious processes, systemic risk and dynamic control. Professor Ozdaglar is the recipient of a Microsoft fellowship, the MIT Graduate Student Council Teaching award, the NSF Career award, the 2008 Donald P. Eckman award of the American Automatic Control Council, the Class of 1943 Career Development Chair, the inaugural Steven and Renee Innovation Fellowship, and the 2014 Spira teaching award. She served on the Board of Governors of the Control System Society in 2010 and was an associate editor for IEEE Transactions on Automatic Control. She is currently the area co-editor for a new area for the journal Operations Research, entitled "Games, Information and Networks. She is the co-author of the book entitled “Convex Analysis and Optimization” (Athena Scientific, 2003).

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