In this paper, we examine a networked multi-agent system running the consensus protocol susceptible to misinformation from its environment. The influenced dynamics are modeled with leader-follower dynamics and the impact of the foreign input is measured through the open loop H₂ norm of the network dynamics. To dampen the external disturbances a novel decentralized edge reweighting method is proposed. The method is composed of a decentralized conjugate gradient method coupled with a decentralized online optimization algorithm. The uncertainties of the effect of local rewiring and unknown environmental influences are demonstrated to be well-suited to the online regret framework. A simulation of the reweighting method is discussed and shown to have a small regret.