Robustness in Consensus Networks
Provides a theoretical foundation for understanding performance scaling in distributed optimization networks, unifying and extending prior convergence results.
The paper provides a formal framework linking robustness (scaling of performance measures like H2-norm) and convergence speed in large consensus networks, deriving tight bounds that hold regardless of network topology.
We consider the problem of robustness in large consensus networks that occur in many areas such as distributed optimization. Robustness, in this context, is the scaling of performance measures, e.g. H2-norm, as a function of network dimension. We provide a formal framework to quantify the relation between such performance scaling and the convergence speed of the network. Specifically, we provide upper and lower bounds for the convergence speed in terms of robustness and discuss how these bounds scale with the network topology. The main contribution of this work is that we obtain tight bounds, that hold regardless of network topology. The work here also encompasses some results in convergence time analysis in previous literature.