Resilient decentralized optimization in multi-agent networks with data injection attack

Shuhua Yu, Yuan Chen, Soummya Kar

Abstract: This paper studies resilient decentralized optimization over multi-agent networks. In particular, we consider the scenario where all networked agents are supposed to parallelly minimize the same objective function with a unique minimizer, but some agents are under data injection attack that perturb their minimizers away from the true minimizer. The goal is to ensure that all agents resiliently recover the true minimizer. We propose a consensus+innovations type of algorithm with signed innovations, to track the coordinate-wise median of all local (possibly perturbed) minimizers. We assume that all local iterates are sublinearly convergent, and the inter-agent undirected communication network is connected on average. We show that, as long as at least one agent is unattacked, and the median of all local minimizers is the true minimizer, the proposed decentralized algorithm asymptotically converges to the true minimizer almost surely at an sublinear rate. Numerical experiments are provided to demonstrate the effectiveness of the algorithm.