Rényi Differential Private Proximal ADMM for Distributed Machine Learning

In this paper, we mainly focus on the privacy protection of distributed optimization algorithms, which means some agents cooperates to solve a problem without leakage of private data. Based on the alternating direction multiplier method (ADMM) and in the case that the objective function contains non-smooth terms, we proposed a proximal ADMM-based algorithm. Then, we use Gaussian noise to disturb the primal estimates to ensure the privacy. In addition, the Gaussian noise decays linearly which ensures the exact convergence of the proposed algorithm, and we show that the algorithm is Rényi differential privacy. Moreover, we establish the convergence of the provided privacy preserving algorithm under some general conditions. Finally, a numerical example on a real dataset is conducted to show the performance of the proposed algorithm.