Consider public health officials aiming to spread awareness about a new vaccine in a community interconnected by a social network. How can they distribute information with minimal resources, ensuring community-wide understanding that aligns with the actual facts? This concern mirrors numerous real-world situations. In this paper, we initialize the study of sample complexity in opinion formation to solve this problem. Our model is built on the recognized opinion formation game, where we regard each agent's opinion as a data-derived model parameter, not just a real number as in prior studies. Such an extension offers a wider understanding of opinion formation and ties closely with federated learning. Through this formulation, we characterize the sample complexity bounds for any network and also show asymptotically tight bounds for specific network structures. Intriguingly, we discover optimal strategies often allocate samples inversely to the degree, hinting at vital policy implications. Our findings are empirically validated on both synthesized and real-world networks.

翻译：考虑公共卫生官员在由社交网络连接的社区中推广新疫苗认知的场景：如何以最小资源分发信息，确保社区整体认知与事实相符？此类关切映射了众多现实情境。本文首次将意见形成的样本复杂度研究引入该问题的求解框架。我们的模型基于公认的意见形成博弈，其中每个智能体的意见被视作数据驱动的模型参数，而非先前研究中单一的实数。这一扩展提供了对意见形成的更广泛理解，并与联邦学习紧密关联。通过该公式化方法，我们刻画了任意网络下的样本复杂度边界，同时针对特定网络结构给出了渐进紧界。引人注目的是，我们发现最优策略往往以节点度的反比分配样本，这暗示了重要的政策启示。我们的发现通过合成网络与真实网络得到了实证验证。