Secure local filtering algorithms for distributed optimization
Shreyas Sundaram, Bahman Gharesifard · 2016
We study a class of local filtering algorithms for consensus-based distributed optimization in the presence of faulty or adversarial nodes. These algorithms do not require the regular nodes to know anything about the global network (other than their own neighbors), and are thus highly scalable. For this class of algorithms, we provide graph-theoretic conditions that guarantee consensus among the regular nodes under various bounds on the number of adversarial nodes (either across the entire network, or in the local neighborhood of any regular node). We prove that a consequence of reaching consensus is that the states of the regular nodes converge to the convex hull of the minimizers of their individual functions, regardless of the actions taken by the adversarial nodes.