Differentially Private Distributed Optimization Over Time-Varying Unbalanced Networks With Linear Convergence Rates

This paper addresses the distributed optimization problem with privacy concerns over time-varying unbalanced networks, where agents collaborate to optimize the average of local objective functions while preserving the privacy of sensitive information encoded in local functions. To tackle the problem, the paper proposes a differentially private algorithm by exploiting decaying Laplace noise without requiring bounded gradients. The proposed algorithm is demonstrated to achieve linear convergence to the sub-optimal solution determined by the noise injected to gradient estimations in mean square and ensure $\epsilon$-differential privacy (DP) of local functions under carefully designed noise parameters. The inherent privacy-accuracy trade-off is revealed through both theoretical insights and simulation results. Furthermore, the image classification and deblurring problems are effectively solved with sensitive data being strictly protected through the deployment of the proposed algorithm, demonstrating the convergence and privacy-preserving performance of the algorithm.