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Analysis of Asynchronous Federated Learning: Unraveling the Interactions between Gradient Compression, Delay, and Data Heterogeneity

Diying Yang, Yingwei Hou, Weigang Wu

TL;DR

The paper addresses the challenge of reducing communication in federated learning by integrating biased gradient compression and error feedback (EF) into asynchronous FL, while accounting for asynchronous delay, data heterogeneity, and flexible client participation. It develops convergences analyses for three frameworks—AsynFL, AsynFLC, and AsynFLC-EF—showing that EF can restore the convergence rate of the full-precision baseline under compression and delays, and providing explicit rates such as $O(1/\sqrt{TKn})$ in suitable regimes. The work reveals a nonlinear interaction between delay and data heterogeneity that exacerbates compression errors, and demonstrates that EF mitigates variance, enabling AsynFLC-EF to achieve the same rate as AsynFL with reduced communication. Extensive experiments on MNIST, FMNIST, and CIFAR-10 validate the theory, showing faster convergence and dramatic communication reductions (e.g., up to $860\times$), while highlighting that compression without EF can hinder convergence on non-IID data. Overall, the study delivers a principled, practical framework for efficient, asynchronous FL with biased compression and EF, supported by rigorous theory and empirical results.

Abstract

In practical federated learning (FL), the large communication overhead between clients and the server is often a significant bottleneck. Gradient compression methods can effectively reduce this overhead, while error feedback (EF) restores model accuracy. Moreover, due to device heterogeneity, synchronous FL often suffers from stragglers and inefficiency-issues that asynchronous FL effectively alleviates. However, in asynchronous FL settings-which inherently face three major challenges: asynchronous delay, data heterogeneity, and flexible client participation-the complex interactions among these system/statistical constraints and compression/EF mechanisms remain poorly understood theoretically. In this paper, we fill this gap through a comprehensive convergence study that adequately decouples and unravels these complex interactions across various FL frameworks. We first consider a basic asynchronous FL framework AsynFL, and establish an improved convergence analysis that relies on fewer assumptions and yields a superior convergence rate than prior studies. We then extend our study to a compressed version, AsynFLC, and derive sufficient conditions for its convergence, indicating the nonlinear interaction between asynchronous delay and compression rate. Our analysis further demonstrates how asynchronous delay and data heterogeneity jointly exacerbate compression-induced errors, thereby hindering convergence. Furthermore, we study the convergence of AsynFLC-EF, the framework that further integrates EF. We prove that EF can effectively reduce the variance of gradient estimation under the aforementioned challenges, enabling AsynFLC-EF to match the convergence rate of AsynFL. We also show that the impact of asynchronous delay and flexible participation on EF is limited to slowing down the higher-order convergence term. Experimental results substantiate our analytical findings very well.

Analysis of Asynchronous Federated Learning: Unraveling the Interactions between Gradient Compression, Delay, and Data Heterogeneity

TL;DR

The paper addresses the challenge of reducing communication in federated learning by integrating biased gradient compression and error feedback (EF) into asynchronous FL, while accounting for asynchronous delay, data heterogeneity, and flexible client participation. It develops convergences analyses for three frameworks—AsynFL, AsynFLC, and AsynFLC-EF—showing that EF can restore the convergence rate of the full-precision baseline under compression and delays, and providing explicit rates such as in suitable regimes. The work reveals a nonlinear interaction between delay and data heterogeneity that exacerbates compression errors, and demonstrates that EF mitigates variance, enabling AsynFLC-EF to achieve the same rate as AsynFL with reduced communication. Extensive experiments on MNIST, FMNIST, and CIFAR-10 validate the theory, showing faster convergence and dramatic communication reductions (e.g., up to ), while highlighting that compression without EF can hinder convergence on non-IID data. Overall, the study delivers a principled, practical framework for efficient, asynchronous FL with biased compression and EF, supported by rigorous theory and empirical results.

Abstract

In practical federated learning (FL), the large communication overhead between clients and the server is often a significant bottleneck. Gradient compression methods can effectively reduce this overhead, while error feedback (EF) restores model accuracy. Moreover, due to device heterogeneity, synchronous FL often suffers from stragglers and inefficiency-issues that asynchronous FL effectively alleviates. However, in asynchronous FL settings-which inherently face three major challenges: asynchronous delay, data heterogeneity, and flexible client participation-the complex interactions among these system/statistical constraints and compression/EF mechanisms remain poorly understood theoretically. In this paper, we fill this gap through a comprehensive convergence study that adequately decouples and unravels these complex interactions across various FL frameworks. We first consider a basic asynchronous FL framework AsynFL, and establish an improved convergence analysis that relies on fewer assumptions and yields a superior convergence rate than prior studies. We then extend our study to a compressed version, AsynFLC, and derive sufficient conditions for its convergence, indicating the nonlinear interaction between asynchronous delay and compression rate. Our analysis further demonstrates how asynchronous delay and data heterogeneity jointly exacerbate compression-induced errors, thereby hindering convergence. Furthermore, we study the convergence of AsynFLC-EF, the framework that further integrates EF. We prove that EF can effectively reduce the variance of gradient estimation under the aforementioned challenges, enabling AsynFLC-EF to match the convergence rate of AsynFL. We also show that the impact of asynchronous delay and flexible participation on EF is limited to slowing down the higher-order convergence term. Experimental results substantiate our analytical findings very well.
Paper Structure (18 sections, 8 theorems, 18 equations, 5 figures, 3 tables)

This paper contains 18 sections, 8 theorems, 18 equations, 5 figures, 3 tables.

Table of Contents

  1. Introduction
  2. Related Work
  3. Convergence Analysis of asynchronous FL
  4. Gradient Compression and Analysis
  5. EF and Analysis
  6. Asynchronous FL Framework
  7. AsynFL
  8. AsynFLC
  9. AsynFLC-EF
  10. Convergence Analysis
  11. Assumptions and Definitions
  12. Convergence Analysis of AsynFL
  13. Convergence Analysis of AsynFLC
  14. Convergence Analysis of AsynFLC-EF
  15. Experiments
  16. ...and 3 more sections

Key Result

Theorem 1

(Convergence of AsynFL). Suppose Assumption ass:1 and Assumption ass:2 hold. If the local learning rates satisfy $\eta \leq \frac{1}{36 \sqrt{2} \tau_{max}^{1.5} \eta_g K L}$, AsynFL satisfies: where $\mathbf{x}^{*}=arg \min f(\mathbf{x})$, $\lambda_1= 72\tau_{avg_0} + 144 \tau_{avg_0} \tau_{max} \eta^2 K^2 L^2$, $\lambda_2=( 18 \tau_{avg_0} \tau_{max} + 144 \tau_{max} \tau_{avg_1} ) \eta^

Figures (5)

  • Figure 1: Comparison of the accuracy and loss of FedBuff, AsynFL, AsynFLC(top3), AsynFLC-EF(top3), AsynFLC(Q4b), and AsynFLC-EF(top3+Q4b) on MNIST(MLP), FMNIST(MLP), CIFAR-10(CNN), and CIFAR-10(AlexNet).
  • Figure 2: Comparison of the accuracy and loss of FedBuff, AsynFL, AsynFLC-EF(top3), AsynFLC-EF(top6), and AsynFLC-EF(top10) on MNIST(MLP), FMNIST(MLP), CIFAR-10(CNN), and CIFAR-10(AlexNet).
  • Figure 3: Comparison of the accuracy and loss of FedBuff, AsynFL, AsynFLC-EF(top6+Q4b), AsynFLC-EF(top10+Q4b), AsynFLC-EF(top3+Q2b), AsynFLC-EF(top3+Q4b), and AsynFLC-EF(top3+Q8b) on MNIST(MLP), FMNIST(MLP), CIFAR-10(CNN), and CIFAR-10(AlexNet).
  • Figure 4: Comparison of the accuracy and loss of FedBuff, AsynFL(500s), AsynFLC-EF(300s), AsynFLC-EF(500s), AsynFLC-EF(700s), and AsynFLC-EF(900s) on MNIST(MLP), FMNIST(MLP), CIFAR-10(CNN), and CIFAR-10(AlexNet).
  • Figure 5: Comparison of the accuracy and loss of AsynFLC(signSGD)-iid/noniid, AsynFLC(top3)-iid/noniid. (a) MLP trained on MNIST, (b) MLP trained on FMNIST, (c) CNN trained on CIFAR-10, and (d) AlexNet trained on CIFAR-10.

Theorems & Definitions (14)

  • Definition 1
  • Definition 2
  • Definition 3
  • Definition 4
  • Theorem 1
  • Corollary 1
  • Remark 1
  • Theorem 2
  • Corollary 2
  • Remark 2
  • ...and 4 more