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 the scenario where some clients may be unavailable during training. Experimental 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）是近期出现的一种用于多客户端间协同模型训练的分布式方法。在SFL中，一个全局模型通常被分割为两部分：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。尽管近期已有关于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双步调更新，SFL的分析可能比联邦学习（FL）更具挑战性。我们针对异构数据上的强凸和一般凸目标函数提供了SFL的收敛性分析。其收敛速率分别为$O(1/T)$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，以及训练过程中部分客户端可能不可用的场景。实验验证了我们的理论结果，并表明当数据在大量客户端间高度异构时，SFL的性能优于FL和分裂学习（SL）。