Distributed Hypothesis Testing and Social Learning in Finite Time with a Finite Amount of Communication
This addresses the problem of efficient distributed decision-making in networked systems, but it is incremental as it builds on prior asymptotic methods.
The paper tackles the problem of distributed hypothesis testing in networks, showing that existing asymptotic learning algorithms can be modified for finite-time learning with a simple binary vector exchange, and further modified to allow all agents to learn and stop transmitting after a finite number of steps.
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.