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