We consider the problem of information aggregation in federated decision making, where a group of agents collaborate to infer the underlying state of nature without sharing their private data with the central processor or each other. We analyze the non-Bayesian social learning strategy in which agents incorporate their individual observations into their opinions (i.e., soft-decisions) with Bayes rule, and the central processor aggregates these opinions by arithmetic or geometric averaging. Building on our previous work, we establish that both pooling strategies result in asymptotic normality characterization of the system, which, for instance, can be utilized in order to give approximate expressions for the error probability. We verify the theoretical findings with simulations and compare both strategies.

翻译：摘要：本文研究了联邦决策中的信息聚合问题，其中一组智能体在无需向中央处理器或彼此共享私有数据的情况下，协作推断自然状态的潜在特征。我们分析了非贝叶斯社会学习策略，该策略中智能体通过贝叶斯规则将其个体观测信息整合至自身观点（即软决策），而中央处理器则通过算术平均或几何平均聚合这些观点。基于前期研究成果，我们证明了两种聚合策略均能实现系统的渐近正态性表征，该特性可被用于推导误差概率的近似表达式。我们通过仿真验证了理论发现，并对两种策略进行了比较。