We study the asymptotic learning rates under linear and log-linear combination rules of belief vectors in a distributed hypothesis testing problem. We show that under both combination strategies, agents are able to learn the truth exponentially fast, with a faster rate under log-linear fusion. We examine the gap between the rates in terms of network connectivity and information diversity. We also provide closed-form expressions for special cases involving federated architectures and exchangeable networks.
翻译:我们在一个分布式假设测试问题中研究信仰矢量线性和日志-线性混合规则下的非现成学习率。我们表明,在两种组合战略下,代理商能够快速地快速地了解真相,在日志-线性聚合下,学习速度更快。我们研究了网络连通率和信息多样性之间的差距。我们还为涉及联邦建筑和可交换网络的特殊案例提供了封闭式表达方式。