Convergence Analysis of Split Federated Learning on Heterogeneous Data

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.

When MiniBatch SGD Meets SplitFed Learning:Convergence Analysis and Performance Evaluation

Federated learning (FL) enables collaborative model training across distributed clients (e.g., edge devices) without sharing raw data. Yet, FL can be computationally expensive as the clients need to train the entire model multiple times. SplitFed learning (SFL) is a recent distributed approach that alleviates computation workload at the client device by splitting the model at a cut layer into two parts, where clients only need to train part of the model. However, SFL still suffers from the \textit{client drift} problem when clients' data are highly non-IID. To address this issue, we propose MiniBatch-SFL. This algorithm incorporates MiniBatch SGD into SFL, where the clients train the client-side model in an FL fashion while the server trains the server-side model similar to MiniBatch SGD. We analyze the convergence of MiniBatch-SFL and show that the bound of the expected loss can be obtained by analyzing the expected server-side and client-side model updates, respectively. The server-side updates do not depend on the non-IID degree of the clients' datasets and can potentially mitigate client drift. However, the client-side model relies on the non-IID degree and can be optimized by properly choosing the cut layer. Perhaps counter-intuitive, our empirical result shows that a latter position of the cut layer leads to a smaller average gradient divergence and a better algorithm performance. Moreover, numerical results show that MiniBatch-SFL achieves higher accuracy than conventional SFL and FL. The accuracy improvement can be up to 24.1\% and 17.1\% with highly non-IID data, respectively.