Communication-efficient Vertical Federated Learning via Compressed Error Feedback

TL;DR

This paper introduces EF-VFL, a communication-efficient vertical federated learning method using error feedback, achieving faster convergence rates and supporting private labels, with strong theoretical guarantees and experimental validation.

Contribution

We propose EF-VFL, a novel error feedback approach for vertical federated learning that improves convergence rates and supports private labels, surpassing prior methods.

Findings

Achieves $ ext{O}(1/T)$ convergence rate for smooth nonconvex problems.

Supports linear convergence under Polyak-{ extL}ojasiewicz condition.

Numerical experiments confirm significant performance improvements.

Abstract

Communication overhead is a known bottleneck in federated learning (FL). To address this, lossy compression is commonly used on the information communicated between the server and clients during training. In horizontal FL, where each client holds a subset of the samples, such communication-compressed training methods have recently seen significant progress. However, in their vertical FL counterparts, where each client holds a subset of the features, our understanding remains limited. To address this, we propose an error feedback compressed vertical federated learning (EF-VFL) method to train split neural networks. In contrast to previous communication-compressed methods for vertical FL, EF-VFL does not require a vanishing compression error for the gradient norm to converge to zero for smooth nonconvex problems. By leveraging error feedback, our method can achieve a $\mathcal{O}(1/T)$ convergence rate for a sufficiently large batch size, improving over the state-of-the-art $\mathcal{O}(1/\sqrt{T})$ rate under $\mathcal{O}(1/\sqrt{T})$ compression error, and matching the rate of uncompressed methods. Further, when the objective function satisfies the Polyak-{\L}ojasiewicz inequality, our method converges linearly. In addition to improving convergence, our method also supports the use of private labels. Numerical experiments show that EF-VFL significantly improves over the prior art, confirming our theoretical results. The code for this work can be found at https://github.com/Valdeira/EF-VFL.