Federated learning has attracted increasing attention with the emergence of distributed data. While extensive federated learning algorithms have been proposed for the non-convex distributed problem, federated learning in practice still faces numerous challenges, such as the large training iterations to converge since the sizes of models and datasets keep increasing, and the lack of adaptivity by SGD-based model updates. Meanwhile, the study of adaptive methods in federated learning is scarce and existing works either lack a complete theoretical convergence guarantee or have slow sample complexity. In this paper, we propose an efficient adaptive algorithm (i.e., FAFED) based on the momentum-based variance-reduced technique in cross-silo FL. We first explore how to design the adaptive algorithm in the FL setting. By providing a counter-example, we prove that a simple combination of FL and adaptive methods could lead to divergence. More importantly, we provide a convergence analysis for our method and prove that our algorithm is the first adaptive FL algorithm to reach the best-known samples $O(\epsilon^{-3})$ and $O(\epsilon^{-2})$ communication rounds to find an $\epsilon$-stationary point without large batches. The experimental results on the language modeling task and image classification task with heterogeneous data demonstrate the efficiency of our algorithms.

翻译：联邦学习随着分布式数据的出现而日益受到关注。尽管针对非凸分布式问题已提出了大量联邦学习算法，但在实践中，联邦学习仍面临诸多挑战，例如由于模型和数据集规模不断增大导致的训练迭代次数过多，以及基于SGD的模型更新缺乏自适应性。与此同时，联邦学习中自适应方法的研究相对匮乏，现有工作要么缺乏完整的理论收敛性保证，要么样本复杂度较高。本文提出了一种基于动量方差缩减技术的跨机构联邦学习高效自适应算法（即FAFED）。我们首先探索如何在联邦学习场景下设计自适应算法。通过提供一个反例，我们证明了简单组合联邦学习与自适应方法可能导致发散。更重要的是，我们对所提方法进行了收敛性分析，并证明该算法是首个无需大batch即可达到已知最优样本复杂度$O(\epsilon^{-3})$和通信轮数$O(\epsilon^{-2})$、找到$\epsilon$-稳定点的自适应联邦学习算法。在异构数据下的语言建模任务和图像分类任务上的实验结果验证了算法的有效性。