Jorge Cortés
Professor
Cymer Corporation Endowed Chair
Differentially private distributed convex
optimization via objective perturbation
E. Nozari, P. Tallapragada, J. Cortés
Proceedings of the American Control
Conference, Boston, Massachusetts, USA, 2016, pp. 2061-2066
Abstract
This paper studies the problem of differentially private distributed
convex unconstrained optimization for multi-agent systems. A group
of agents seek to minimize the aggregate sum of their individual
objective functions. Each agent only knows its own objective
function and wants to keep it private from other agents or
eavesdroppers listening to the network communications. Our design
strategy consists of perturbing the objective functions with Laplace
noise so that any query on the functions or their attributes is
differentially private. This, together with the fact that
differential privacy is immune to post-processing, allows us to
employ any distributed algorithm that solves the unconstrained
convex optimization problem on the perturbed objective
functions. Our technical approach carefully describes how these
perturbations can be selected so that the resulting functions retain
the requirements on smoothness and convexity critical to many
optimization algorithms. We quantify the magnitude of the expected
deviation of the algorithm output from the true optimizer. The
specific choice of distributed optimization algorithm determines the
requirements on the network communication graph. Simulations
illustrate the strengths of the proposed approach.
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Mechanical and Aerospace Engineering,
University of California, San Diego
9500 Gilman Dr,
La Jolla, California, 92093-0411
Ph: 1-858-822-7930
Fax: 1-858-822-3107
cortes at ucsd.edu
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