Federated learning (FL) is increasingly adopted in domains like healthcare, where data privacy is paramount. A fundamental challenge in these systems is statistical heterogeneity-the fact that data distributions vary significantly across clients (e.g., different hospitals may treat distinct patient demographics). While current FL algorithms focus on aggregating model updates from these heterogeneous clients, the potential of the central server remains under-explored. This paper is motivated by a healthcare scenario: could a central server not only coordinate model training but also guide a new patient to the hospital best equipped for their specific condition? We generalize this idea to propose a novel paradigm for FL systems where the server actively guides the allocation of new tasks or queries to the most appropriate client. To enable this, we introduce a density ratio model and empirical likelihood-based framework that simultaneously addresses two goals: (1) learning effective local models on each client, and (2) finding the best matching client for a new query. Empirical results demonstrate the framework's effectiveness on benchmark datasets, showing improvements in both model accuracy and the precision of client guidance compared to standard FL approaches. This work opens a new direction for building more intelligent and resource-efficient FL systems that leverage heterogeneity as a feature, not just a bug. Code is available at https://github.com/zijianwang0510/FedDRM.git.

翻译：联邦学习（FL）在医疗健康等数据隐私至关重要的领域日益普及。这些系统面临的一个根本性挑战是统计异质性——即不同客户端（例如不同医院可能服务于不同的患者群体）之间的数据分布存在显著差异。当前FL算法主要聚焦于聚合来自这些异构客户端的模型更新，而中央服务器的潜力尚未得到充分探索。本文受一个医疗场景启发：中央服务器能否不仅协调模型训练，还能将新患者引导至最适合其特定病情的医院？我们将这一思想推广，提出一种新颖的FL系统范式，其中服务器主动引导新任务或查询分配给最合适的客户端。为实现这一目标，我们引入了一种基于密度比模型和经验似然的框架，该框架同时解决两个目标：（1）在每个客户端上学习有效的本地模型；（2）为新的查询找到最佳匹配的客户端。在基准数据集上的实证结果表明，与标准FL方法相比，该框架在模型准确性和客户端引导精度方面均有所提升。这项工作为构建更智能、资源效率更高的FL系统开辟了新方向，将异质性视为一种特性而非缺陷。代码发布于 https://github.com/zijianwang0510/FedDRM.git。