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：我们研究了分布式假设检验问题中信念向量在线性及对数线性组合规则下的渐近学习速率。我们证明，两种组合策略均能使智能体以指数速度学习真相，其中对数线性融合策略下的速率更快。我们基于网络连通性与信息多样性分析了速率差异，并针对联邦架构与可交换网络等特例给出了闭式解。