有限时间有限通信量下的分布式假设检验与社会学习
Distributed Hypothesis Testing and Social Learning in Finite Time with a Finite Amount of Communication
摘要：
我们考虑分布式假设检验（或社会学习）的问题，其中代理网络试图从一组有限的假设中识别世界的真实状态，基于每个代理接收到的一系列随机信号。关于这个问题的先前工作提供了分布式算法，保证渐近学习的真实状态，相应的努力，以提高学习速度。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，使学习在有限的时间内，有效地产生任意大的（渐近）率。然后，我们提供了一个简单的算法有限时间学习，只需要代理交换一个二进制向量（长度等于可能的假设的数量）与他们的邻居在每个时间步。最后，我们证明了，如果代理知道网络的直径，我们的算法可以进一步修改，以允许所有代理学习真实状态，并在有限数量的时间步长后停止向邻居传输。
英文摘要：
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.
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