Federated learning (FL) provides a communication-efficient approach to solve machine learning problems concerning distributed data, without sending raw data to a central server. However, existing works on FL only utilize first-order gradient descent (GD) and do not consider the preceding iterations to gradient update which can potentially accelerate convergence. In this article, we consider momentum term which relates to the last iteration. The proposed momentum federated learning (MFL) uses momentum gradient descent (MGD) in the local update step of FL system. We establish global convergence properties of MFL and derive an upper bound on MFL convergence rate. Comparing the upper bounds on MFL and FL convergence rates, we provide conditions in which MFL accelerates the convergence. For different machine learning models, the convergence performance of MFL is evaluated based on experiments with MNIST and CIFAR-10 datasets. Simulation results confirm that MFL is globally convergent and further reveal significant convergence improvement over FL.

中文翻译：

---

通过动量梯度下降加速联邦学习

联邦学习 (FL) 提供了一种通信高效的方法来解决有关分布式数据的机器学习问题，而无需将原始数据发送到中央服务器。然而，现有的 FL 工作仅利用一阶梯度下降 (GD)，并没有考虑之前的迭代梯度更新，这可能会加速收敛。在本文中，我们考虑与最后一次迭代相关的动量项。提议的动量联邦学习 (MFL) 在 FL 系统的局部更新步骤中使用动量梯度下降 (MGD)。我们建立了 MFL 的全局收敛特性并推导出 MFL 收敛率的上限。比较 MFL 和 FL 收敛速率的上限，我们提供了 MFL 加速收敛的条件。对于不同的机器学习模型，MFL 的收敛性能是基于 MNIST 和 CIFAR-10 数据集的实验评估的。仿真结果证实 MFL 是全局收敛的，并进一步揭示了对 FL 的显着收敛改进。