A Privacy-Preserving Finite-Time Push-Sum based Gradient Method for Distributed Optimization over Digraphs

This paper addresses the problem of distributed optimization, where a network agents represented as directed graph (digraph) aims to collaboratively minimize sum their individual cost functions. Existing approaches for optimization over digraphs, such Push-Pull, require exchange explicit state values with neighbors in order reach an optimal solution. However, this can result disclosure sensitive and private information. To overcome issue, we propose state-decomposition-based privacy-preserving finite-time push-sum (PrFTPS) algorithm without any global information, size or diameter. Then, based on PrFTPS, design gradient descent (PrFTPS-GD) solve problem. It is proved that under PrFTPS-GD, privacy each agent preserved linear convergence rate related iteration number achieved. Finally, numerical simulations are provided illustrate effectiveness proposed approach.