Federated Learning (FL) has emerged as a powerful paradigm for decentralized machine learning, enabling collaborative model training across diverse clients without sharing raw data. However, traditional FL approaches often face limitations in scalability and efficiency due to their reliance on synchronous client updates, which can result in significant delays and increased communication overhead, particularly in heterogeneous and dynamic environments. To address these challenges in this paper, we propose an Asynchronous Federated Learning (AFL) algorithm, which allows clients to update the global model independently and asynchronously. Our key contributions include a comprehensive convergence analysis of AFL in the presence of client delays and model staleness. By leveraging martingale difference sequence theory and variance bounds, we ensure robust convergence despite asynchronous updates. Assuming strongly convex local objective functions, we establish bounds on gradient variance under random client sampling and derive a recursion formula quantifying the impact of client delays on convergence. Furthermore, we demonstrate the practical applicability of AFL by training a decentralized Long Short-Term Memory (LSTM)-based deep learning model on the CMIP6 climate dataset, effectively handling non-IID and geographically distributed data. The proposed AFL algorithm addresses key limitations of traditional FL methods, such as inefficiency due to global synchronization and susceptibility to client drift. It enhances scalability, robustness, and efficiency in real-world settings with heterogeneous client populations and dynamic network conditions. Our results underscore the potential of AFL to drive advancements in distributed learning systems, particularly for large-scale, privacy-preserving applications in resource-constrained environments.

翻译：联邦学习（FL）已成为一种强大的去中心化机器学习范式，能够在不同客户端之间实现协同模型训练而无需共享原始数据。然而，传统联邦学习方法由于依赖同步的客户端更新，在可扩展性和效率方面常面临局限，这可能导致显著的延迟和通信开销增加，尤其在异构和动态环境中更为突出。为应对这些挑战，本文提出一种异步联邦学习（AFL）算法，该算法允许客户端独立且异步地更新全局模型。我们的核心贡献包括在存在客户端延迟和模型陈旧性的情况下对AFL进行的全面收敛性分析。通过利用鞅差序列理论和方差界限，我们确保了异步更新下的稳健收敛。在假设局部目标函数强凸的前提下，我们建立了随机客户端采样下的梯度方差界限，并推导出量化客户端延迟对收敛影响的递归公式。此外，我们通过在CMIP6气候数据集上训练一个基于长短期记忆（LSTM）网络的去中心化深度学习模型，验证了AFL的实际适用性，有效处理了非独立同分布和地理分布的数据。所提出的AFL算法解决了传统联邦学习方法的关键局限，例如因全局同步导致的低效性和对客户端漂移的敏感性。它在具有异构客户端群体和动态网络条件的实际场景中，显著提升了可扩展性、鲁棒性和效率。我们的研究结果凸显了AFL在推动分布式学习系统发展方面的潜力，尤其适用于资源受限环境下的大规模隐私保护应用。