Differentially Private Distributed Convex Optimization via Functional Perturbation

We study a class of distributed convex constrained optimization problems where a group of agents aim to minimize the sum of individual objective functions while each desires that any information about its objective function is kept private. We prove the impossibility of achieving differential privac...

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Bibliographic Details
Published in:IEEE transactions on control of network systems Vol. 5; no. 1; pp. 395 - 408
Main Authors: Nozari, Erfan, Tallapragada, Pavankumar, Cortes, Jorge
Format: Journal Article
Language:English
Published: IEEE 01.03.2018
Subjects:
Algorithm design and analysis
Convex functions
Cyber-physical systems
differential privacy
distributed algorithms/control
Heuristic algorithms
Hilbert space
Linear programming
networks of autonomous agents
Optimization
Privacy
ISSN:2325-5870, 2372-2533
Online Access:Get full text
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Summary:We study a class of distributed convex constrained optimization problems where a group of agents aim to minimize the sum of individual objective functions while each desires that any information about its objective function is kept private. We prove the impossibility of achieving differential privacy using strategies based on perturbing the inter-agent messages with noise when the underlying noise-free dynamics are asymptotically stable. This justifies our algorithmic solution based on the perturbation of individual functions with Laplace noise. To this end, we establish a general framework for differentially private handling of functional data. We further design post-processing steps that ensure the perturbed functions regain the smoothness and convexity properties of the original functions while preserving the differentially private guarantees of the functional perturbation step. This methodology allows us to use any distributed coordination algorithm to solve the optimization problem on the noisy functions. Finally, we explicitly bound the magnitude of the expected distance between the perturbed and true optimizers which leads to an upper bound on the privacy-accuracy tradeoff curve. Simulations illustrate our results.
ISSN:2325-5870
2372-2533
DOI:10.1109/TCNS.2016.2614100