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

A Communication-Efficient Algorithm for Exponentially Fast Non-Bayesian Learning in Networks