Privacy-Protected Decentralized Dual Averaging Push With Edge-Based Correlated Perturbations Over Time-Varying Directed Networks

Abstract

In this article, we consider a decentralized constrained optimization problem over time-varying directed networks, where nodes in the networks collaboratively minimize the sum of local cost functions subject to a common constraint set. Due to the continued broadcasting of information that involves privacy during the optimization process, most existing decentralized algorithms for settling the problem may suffer from the risk of privacy leakage of normal nodes. The problem becomes even more challenging when the networks are time-varying and directed. To overcome these difficulties, we propose an effective privacy-protected decentralized dual averaging push algorithm that possesses two appealing features. On the one hand, our algorithm adds edge-based correlated perturbation signals to the process of information transmission for protecting privacy. On the other hand, our algorithm involves the use of the push-sum averaging protocol which can overcome the impact of the imbalance caused by time-varying directed networks. We provide rigorous analyses for convergence and privacy protection to illustrate that our algorithm not only protects the privacy of normal nodes but also converges exactly to the optimal solution under weaker initial conditions than the existing decentralized works. Numerical examples are given to demonstrate the viability and performance of our algorithm.