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 to derive approximate expressions for the error probability. We verify the theoretical findings with simulations and compare both strategies.

翻译：我们考虑联邦决策中的信息聚合问题，其中一组智能体通过协作推断自然状态的潜在本质，同时避免向中心处理器或彼此之间共享私有数据。我们分析了非贝叶斯社会学习策略：智能体利用贝叶斯规则将个体观测融入其观点（即软决策），而中心处理器则通过算术平均或几何平均聚合这些观点。基于先前工作，我们证明两种聚合策略均能使系统呈现渐近正态性特征——例如，该特性可用于推导误差概率的近似表达式。我们通过仿真验证理论结果，并对两种策略进行比较。