In this paper, we study the fundamental limits of hierarchical secure aggregation under unreliable communication. We consider a hierarchical network where each client connects to multiple relays, and both client-to-relay and relay-to-server links are intermittent. Under this setting, we characterize the minimum communication and randomness costs required to achieve robust secure aggregation. We then propose an optimal protocol that attains these minimum costs, and establish its optimality through a matching converse proof. In addition, we introduce an improved problem formulation that bridges the gap between existing information-theoretic secure aggregation protocols and practical real-world federated learning problems.

翻译：本文研究了不可靠通信条件下分层安全聚合的基本极限。我们考虑一个分层网络结构，其中每个客户端连接至多个中继节点，且客户端-中继链路与中继-服务器链路均存在间歇性中断。在此设定下，我们刻画了实现鲁棒安全聚合所需的最小通信成本与随机性成本。随后，我们提出了一种达到这些最小成本的最优协议，并通过匹配的逆证明确立了其最优性。此外，我们提出了一种改进的问题建模方法，以弥合现有信息论安全聚合协议与实际联邦学习问题之间的差距。