Differentially Private Distributed Optimization Over Diagraphs With Application to Image Deblurring

Abstract

This article investigates the distributed optimization problem over directed graphs, where agents work together to minimize the average of local objective functions. To protect private information from potential eavesdroppers in communication networks, we propose an algorithm that employs decaying Laplace noise, ensuring differential privacy in directed networks. Without assuming bounded gradients, the proposed algorithm can achieve both linear convergence in mean square and $\epsilon$-differential privacy over directed networks. A comprehensive analysis of the tradeoff between privacy and accuracy is also provided. Furthermore, the image deblurring task is formulated as a distributed optimization problem, and visually pleasing results obtained by the deployment of the proposed algorithm verify the theoretical claims.