Convergence Analysis of Split Federated Learning on Heterogeneous Data

TL;DR

This paper provides the first convergence analysis of split federated learning (SFL) on heterogeneous data, establishing theoretical rates and validating them through experiments, demonstrating SFL's advantages over FL and SL.

Contribution

It offers the first convergence analysis of SFL for convex and non-convex objectives, including heterogeneous data and client unavailability scenarios.

Findings

SFL converges at rates of O(1/T) for strongly convex and O(1/∛T) for convex objectives.

Experimental results show SFL outperforms FL and SL on highly heterogeneous data.

Theoretical analysis is validated by experiments confirming convergence rates.

Abstract

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.