FedHL: Federated Learning for Heterogeneous Low-Rank Adaptation via Unbiased Aggregation

TL;DR

FedHL introduces a federated learning framework that effectively handles heterogeneous low-rank adaptations by unbiased aggregation, ensuring convergence and improving performance over existing methods.

Contribution

The paper proposes FedHL, a novel federated learning approach that eliminates truncation bias and derives optimal aggregation weights for better convergence with heterogeneous LoRA.

Findings

Guarantees $ ext{O}(1/\sqrt{T})$ convergence rate.

Achieves 1-3% performance improvement over state-of-the-art methods.

Effectively handles client-specific LoRA ranks without truncation bias.

Abstract

Federated Learning (FL) facilitates the fine-tuning of Foundation Models (FMs) using distributed data sources, with Low-Rank Adaptation (LoRA) gaining popularity due to its low communication costs and strong performance. While recent work acknowledges the benefits of heterogeneous LoRA in FL and introduces flexible algorithms to support its implementation, our theoretical analysis reveals a critical gap: existing methods lack formal convergence guarantees due to parameter truncation and biased gradient updates. Specifically, adapting client-specific LoRA ranks necessitates truncating global parameters, which introduces inherent truncation errors and leads to subsequent inaccurate gradient updates that accumulate over training rounds, ultimately degrading performance. To address the above issues, we propose \textbf{FedHL}, a simple yet effective \textbf{Fed}erated Learning framework tailored for \textbf{H}eterogeneous \textbf{L}oRA. By leveraging the full-rank global model as a calibrated aggregation basis, FedHL eliminates the direct truncation bias from initial alignment with client-specific ranks. Furthermore, we derive the theoretically optimal aggregation weights by minimizing the gradient drift term in the convergence upper bound. Our analysis shows that FedHL guarantees $\mathcal{O}(1/\sqrt{T})$ convergence rate, and experiments on multiple real-world datasets demonstrate a 1-3\% improvement over several state-of-the-art methods.