Privacy Preserving Modified Projection Subgradient Algorithm for Multi-Agent Online Optimization

Abstract

This paper studies the distributed online optimization problem with the property of privacy preservation over multi-agent system, where the communication topology is a fixed and strongly connected digraph. We only assume that the weight matrix is row stochastic, which relaxes the assumption of doubly stochastic in some literature and is easier to implement than the column stochastic weight matrix. A virtual agent associated with each agent is added which only communicates with the agent itself and performs gradient iterative update. The original agent only communicates with the original neighbors and virtual agent. A distributed online algorithm is designed by using gradient readjustment technology combined with distributed projection subgradient method. It is proved that the proposed algorithm can achieve the purpose of privacy preservation while realizing the sublinear regret bound. Finally, an example is provided to validate the performance of the algorithm.