Traditional social learning frameworks consider environments with a homogeneous state, where each agent receives observations conditioned on that true state of nature. In this work, we relax this assumption and study the distributed hypothesis testing problem in a heterogeneous environment, where each agent can receive observations conditioned on their own personalized state of nature (or truth). This situation arises in many scenarios, such as when sensors are spatially distributed, or when individuals in a social network have differing views or opinions. In these heterogeneous contexts, the graph topology admits a block structure. We study social learning under personalized (or multitask) models and examine their convergence behavior.

翻译：传统的社会学习框架考虑具有同质状态的环境，其中每个智能体接收到的观测值均以该真实自然状态为条件。本研究放宽了这一假设，研究了异质环境下的分布式假设检验问题，其中每个智能体可以接收到以其个性化自然状态（或真实状态）为条件的观测值。这种情况出现在许多场景中，例如传感器在空间上分布时，或社交网络中的个体持有不同观点或意见时。在这些异质背景下，图拓扑结构呈现块状结构。我们研究了在个性化（或多任务）模型下的社会学习，并考察了其收敛行为。