Distributed Nesterov Gradient for Differentially Private Optimization with Exact Convergence

Differentially-private distributed optimization algorithms can preserve the private gradient but bring unavoidable trade-off between privacy and optimality. Some methods have been studied to address this based on diminishing stepsize with only sublinear convergence. To improve convergence rate, the exact Differentially-Private algorithm based on the distributed gradient Tracking and distributed Nesterov gradient methods (eDP-TN) with fixed stepsize is proposed to achieve privacy and the accelerated linear convergence to the optimal solution. Leveraging matrix spectrum and Laplace distribution, the linear convergence is established in mean. The privacy level of eDP-TN is also determined based on differential privacy over a finite time horizon. Simulations are conducted on a distributed sensor problem to verify the effectiveness of the theoretical findings.