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We address the problem of learning the legitimacy of other agents in a multiagent network when an unknown subset is comprised of malicious actors. We specifically derive results for the case of directed graphs and where stochastic side information, or observations of trust, is available. We refer to this as “learning trust” since agents must identify which neighbors in the network are reliable, and we derive a protocol to achieve this. We also provide analytical results showing that under this protocol i) agents can learn the legitimacy of all other agents almost surely, and that ii) the opinions of the agents converge in mean to the true legitimacy of all other agents in the network. Lastly, we provide numerical studies showing that our convergence results hold in practice for various network topologies and variations in the number of malicious agents in the network. Keywords: Multiagent systems, adversarial learning, directed graphs, networked 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 focuses on the problem of distributed optimization in multi-agent cyberphysical systems, where a legitimate agent’s dynamic is influenced both by the values it receives from potentially malicious neighboring agents, and by its own self-serving target function. We develop a new algorithmic and analytical framework to achieve resilience for the class of problems where stochastic values of trust between agents exist and can be exploited. In this case we show that convergence to the true global optimal point can be recovered, both in mean and almost surely, even in the presence of malicious agents. Furthermore, we provide expected convergence rate guarantees in the form of upper bounds 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 compose the majority of agents in the network.