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We consider the problem of distributed hypothesis testing (or sociallearning) where a network of agents seeks to identify the true state of theworld from a finite set of hypotheses, based on a series of stochastic signalsthat each agent receives. Prior work on this problem has provided distributedalgorithms that guarantee asymptotic learning of the true state, withcorresponding efforts to improve the rate of learning. In this paper, we firstargue that one can readily modify existing asymptotic learning algorithms toenable learning in finite time, effectively yielding arbitrarily large(asymptotic) rates. We then provide a simple algorithm for finite-time learningwhich only requires the agents to exchange a binary vector (of length equal tothe number of possible hypotheses) with their neighbors at each time-step.Finally, we show that if the agents know the diameter of the network, ouralgorithm can be further modified to allow all agents to learn the true stateand stop transmitting to their neighbors after a finite number of time-steps.

Distributed Hypothesis Testing and Social Learning in Finite Time with a Finite Amount of Communication