3 research outputs found
Differentially Private Convex Optimization with Feasibility Guarantees
This paper develops a novel differentially private framework to solve convex
optimization problems with sensitive optimization data and complex physical or
operational constraints. Unlike standard noise-additive algorithms, that act
primarily on the problem data, objective or solution, and disregard the problem
constraints, this framework requires the optimization variables to be a
function of the noise and exploits a chance-constrained problem reformulation
with formal feasibility guarantees. The noise is calibrated to provide
differential privacy for identity and linear queries on the optimization
solution. For many applications, including resource allocation problems, the
proposed framework provides a trade-off between the expected optimality loss
and the variance of optimization results
Privacy-Preserving Distributed Zeroth-Order Optimization
We develop a privacy-preserving distributed algorithm to minimize a
regularized empirical risk function when the first-order information is not
available and data is distributed over a multi-agent network. We employ a
zeroth-order method to minimize the associated augmented Lagrangian function in
the primal domain using the alternating direction method of multipliers (ADMM).
We show that the proposed algorithm, named distributed zeroth-order ADMM
(D-ZOA), has intrinsic privacy-preserving properties. Unlike the existing
privacy-preserving methods based on the ADMM where the primal or the dual
variables are perturbed with noise, the inherent randomness due to the use of a
zeroth-order method endows D-ZOA with intrinsic differential privacy. By
analyzing the perturbation of the primal variable, we show that the privacy
leakage of the proposed D-ZOA algorithm is bounded. In addition, we employ the
moments accountant method to show that the total privacy leakage grows
sublinearly with the number of ADMM iterations. D-ZOA outperforms the existing
differentially private approaches in terms of accuracy while yielding the same
privacy guarantee. We prove that D-ZOA converges to the optimal solution at a
rate of where is the number of ADMM iterations. The
convergence analysis also reveals a practically important trade-off between
privacy and accuracy. Simulation results verify the desirable
privacy-preserving properties of D-ZOA and its superiority over a
state-of-the-art algorithm as well as its network-wide convergence to the
optimal solution
Local Differential Privacy in Decentralized Optimization
Privacy concerns with sensitive data are receiving increasing attention. In
this paper, we study local differential privacy (LDP) in interactive
decentralized optimization. By constructing random local aggregators, we
propose a framework to amplify LDP by a constant. We take Alternating Direction
Method of Multipliers (ADMM), and decentralized gradient descent as two
concrete examples, where experiments support our theory. In an asymptotic view,
we address the following question: Under LDP, is it possible to design a
distributed private minimizer for arbitrary closed convex constraints with
utility loss not explicitly dependent on dimensionality? As an affiliated
result, we also show that with merely linear secret sharing, information
theoretic privacy is achievable for bounded colluding agents