  We consider the model of cooperative learning via distributed non-Bayesian
learning, where a network of agents tries to jointly agree on a hypothesis that
best described a sequence of locally available observations. Building upon
recently proposed weak communication network models, we propose a robust
cooperative learning rule that allows asynchronous communications, message
delays, unpredictable message losses, and directed communication among nodes.
We show that our proposed learning dynamics guarantee that all agents in the
network will have an asymptotic exponential decay of their beliefs on the wrong
hypothesis, indicating that the beliefs of all agents will concentrate on the
optimal hypotheses. Numerical experiments provide evidence on a number of
network setups.
