  We introduce a simple time-triggered protocol to achieve
communication-efficient non-Bayesian learning over a network. Specifically, we
consider a scenario where a group of agents interact over a graph with the aim
of discerning the true state of the world that generates their joint
observation profiles. To address this problem, we propose a novel distributed
learning rule wherein agents aggregate neighboring beliefs based on a
min-protocol, and the inter-communication intervals grow geometrically at a
rate $a \geq 1$. Despite such sparse communication, we show that each agent is
still able to rule out every false hypothesis exponentially fast with
probability $1$, as long as $a$ is finite. For the special case when
communication occurs at every time-step, i.e., when $a=1$, we prove that the
asymptotic learning rates resulting from our algorithm are network-structure
independent, and a strict improvement upon those existing in the literature. In
contrast, when $a>1$, our analysis reveals that the asymptotic learning rates
vary across agents, and exhibit a non-trivial dependence on the network
topology coupled with the relative entropies of the agents' likelihood models.
This motivates us to consider the problem of allocating signal structures to
agents to maximize appropriate performance metrics. In certain special cases,
we show that the eccentricity centrality and the decay centrality of the
underlying graph help identify optimal allocations; for more general scenarios,
we bound the deviation from the optimal allocation as a function of the
parameter $a$, and the diameter of the communication graph.
