  This work focuses on the problem of distributed optimization in multi-agent
cyberphysical systems, where a legitimate agents' iterates are 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, numerical results are presented that validate our analytical
convergence guarantees even when the malicious agents compose the majority of
agents in the network and where existing methods fail to converge to the
optimal nominal points.
