  We study the convergence of the log-linear non-Bayesian social learning
update rule, for a group of agents that collectively seek to identify a
parameter that best describes a joint sequence of observations. Contrary to
recent literature, we focus on the case where agents assign decaying weights to
its neighbors, and the network is not connected at every time instant but over
some finite time intervals. We provide a necessary and sufficient condition for
the rate at which agents decrease the weights and still guarantees social
learning.
