Federated Domain Adaptation (FDA) describes the federated learning (FL) setting where source clients and a server work collaboratively to improve the performance of a target client where limited data is available. The domain shift between the source and target domains, coupled with limited data of the target client, makes FDA a challenging problem, e.g., common techniques such as federated averaging and fine-tuning fail due to domain shift and data scarcity. To theoretically understand the problem, we introduce new metrics that characterize the FDA setting and a theoretical framework with novel theorems for analyzing the performance of server aggregation rules. Further, we propose a novel lightweight aggregation rule, Federated Gradient Projection ($\texttt{FedGP}$), which significantly improves the target performance with domain shift and data scarcity. Moreover, our theory suggests an $\textit{auto-weighting scheme}$ that finds the optimal combinations of the source and target gradients. This scheme improves both $\texttt{FedGP}$ and a simpler heuristic aggregation rule. Extensive experiments verify the theoretical insights and illustrate the effectiveness of the proposed methods in practice.

翻译：联邦域自适应（FDA）描述了联邦学习（FL）场景，其中源客户端与服务器协作以提升数据有限的目标客户端性能。源域与目标域之间的域偏移，加之目标客户端数据稀缺，使得FDA成为一个具有挑战性的问题——例如，联邦平均和微调等常见技术因域偏移和数据稀少而失效。为从理论上理解该问题，我们引入了表征FDA设置的新指标，并提出了一个包含新颖定理的理论框架，用于分析服务器聚合规则的性能。此外，我们提出了一种轻量级聚合规则——联邦梯度投影（$\texttt{FedGP}$），该规则在域偏移和数据稀缺条件下显著提升了目标性能。更关键的是，我们的理论提出了一种$\textit{自动加权方案}$，能够找到源梯度和目标梯度的最优组合。该方案既改进了$\texttt{FedGP}$，也优化了更简单的启发式聚合规则。大量实验验证了理论见解，并展示了所提方法在实际中的有效性。