Federated learning (FL) aims to minimize the communication complexity of training a model over heterogeneous data distributed across many clients. A common approach is local methods, where clients take multiple optimization steps over local data before communicating with the server (e.g., FedAvg). Local methods can exploit similarity between clients' data. However, in existing analyses, this comes at the cost of slow convergence in terms of the dependence on the number of communication rounds R. On the other hand, global methods, where clients simply return a gradient vector in each round (e.g., SGD), converge faster in terms of R but fail to exploit the similarity between clients even when clients are homogeneous. We propose FedChain, an algorithmic framework that combines the strengths of local methods and global methods to achieve fast convergence in terms of R while leveraging the similarity between clients. Using FedChain, we instantiate algorithms that improve upon previously known rates in the general convex and PL settings, and are near-optimal (via an algorithm-independent lower bound that we show) for problems that satisfy strong convexity. Empirical results support this theoretical gain over existing methods.

翻译：联邦学习旨在最小化在分布式多客户端异构数据上训练模型的通信复杂度。常见方法包括局部方法（如FedAvg），即客户端在与服务器通信前对本地数据执行多次优化步骤。局部方法能利用客户端间数据相似性，但现有分析表明，这会导致收敛速度随通信轮次R的增加而变慢。相反，全局方法（如SGD）中客户端每轮仅返回梯度向量，虽在R维度收敛更快，却无法利用客户端间相似性（即使客户端同质）。我们提出FedChain算法框架，融合局部方法与全局方法优势，在利用客户端相似性的同时实现快速收敛。基于FedChain，我们实例化了在一般凸与PL条件下优于已知速率的算法，并在强凸问题上达到近最优性（通过算法无关下界证明）。实验结果验证了该方法相较于现有方案的理论增益。