Resilience to Malicious Activity in Distributed Optimization for Cyberphysical Systems

Enhancing resilience in distributed networks in the face of malicious agents is an important problem for which many key theoretical results and applications require further development and characterization. This work develops a new algorithmic and analytical framework for achieving resilience to malicious agents in distributed optimization problems where a legitimate agent's dynamic is influenced by the values it receives from neighboring agents and its own self-serving target function. We show that by utilizing stochastic values of trust between agents it is possible to recover convergence to the system's global optimal point even in the presence of malicious agents. Additionally, we provide expected convergence rate guarantees in the form of an upper bound on the expected squared distance to the optimal value. Finally, we present numerical results that validate the analytical convergence guarantees we present in this paper even when the malicious agents are the majority of agents in the network.