Constant-Stepsize Distributed Optimization Algorithm with Malicious Nodes

Abstract

This paper develops a consensus-based distributed (sub)gradient descent algorithm, which has a faster convergence rate in the presence of malicious nodes. To achieve this, two main methods are used in the proposed algorithm. The first is using the local filtering algorithm to counteract the attacks of malicious nodes; The second is using the constant step size in the distributed (sub)gradient descent algorithm rather than diminishing step size to accelerate the convergence rate. As a result, the proposed algorithm improves the convergence rate in the presence of malicious nodes. Finally, a numerical example is presented to verify the proposed algorithm, and the possible future research directions are given.