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.

中文翻译：

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有限通信量的有限时间分布式假设检验和社会学习

我们考虑分布式假设检验（或社会学习）的问题，其中代理网络试图根据每个代理收到的一系列随机信号，从一组有限的假设中识别世界的真实状态。在此问题上的先前工作提供了保证真实状态的渐近学习的分布式算法，并相应地努力提高学习率。在本文中，我们首先认为可以很容易地修改现有的渐近学习算法，以实现在有限时间内学习，有效地产生任意大的（渐近）率。然后我们提供了一个简单的有限时间学习算法，它只需要代理在每个时间步与他们的邻居交换一个二进制向量（长度等于可能的假设数量）。最后，