Split federated learning (SFL) is a recent distributed approach for collaborative model training among multiple clients. In SFL, a global model is typically split into two parts, where clients train one part in a parallel federated manner, and a main server trains the other. Despite the recent research on SFL algorithm development, the convergence analysis of SFL is missing in the literature, and this paper aims to fill this gap. The analysis of SFL can be more challenging than that of federated learning (FL), due to the potential dual-paced updates at the clients and the main server. We provide convergence analysis of SFL for strongly convex and general convex objectives on heterogeneous data. The convergence rates are $O(1/T)$ and $O(1/\sqrt[3]{T})$, respectively, where $T$ denotes the total number of rounds for SFL training. We further extend the analysis to non-convex objectives and where some clients may be unavailable during training. Numerical experiments validate our theoretical results and show that SFL outperforms FL and split learning (SL) when data is highly heterogeneous across a large number of clients.

翻译：分裂联邦学习（SFL）是一种最新的分布式方法，用于多个客户端间的协作模型训练。在SFL中，全局模型通常被分为两部分，客户端以并行联邦方式训练其中一部分，而主服务器训练另一部分。尽管近期有关于SFL算法开发的研究，但文献中尚缺乏对SFL收敛性的分析，本文旨在填补这一空白。由于客户端和主服务器可能存在的双速更新，SFL的分析比联邦学习（FL）更具挑战性。我们针对强凸和一般凸目标函数下的异构数据，提供了SFL的收敛性分析。收敛速度分别为$O(1/T)$和$O(1/\sqrt[3]{T})$，其中$T$表示SFL训练的总轮数。我们进一步将分析扩展到非凸目标函数以及训练中某些客户端可能不可用的情况。数值实验验证了我们的理论结果，并表明当大量客户端的数据高度异构时，SFL优于FL和分裂学习（SL）。