  We study a setting where a group of agents, each receiving partially
informative private signals, seek to collaboratively learn the true underlying
state of the world (from a finite set of hypotheses) that generates their joint
observation profiles. To solve this problem, we propose a distributed learning
rule that differs fundamentally from existing approaches, in that it does not
employ any form of "belief-averaging". Instead, agents update their beliefs
based on a min-rule. Under standard assumptions on the observation model and
the network structure, we establish that each agent learns the truth
asymptotically almost surely. As our main contribution, we prove that with
probability 1, each false hypothesis is ruled out by every agent exponentially
fast at a network-independent rate that is strictly larger than existing rates.
We then develop a computationally-efficient variant of our learning rule that
is provably resilient to agents who do not behave as expected (as represented
by a Byzantine adversary model) and deliberately try to spread misinformation.
