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 paper, 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 rate, 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 dataset. Simulation results
comfirm that MFL is globally convergent and further reveal significant
convergence improvement over FL.

本研究探讨了动量联邦学习在解决分布式数据机器学习问题方面的应用。在本文中，我们提出了一种新的方法来将动量梯度下降算法应用于本地更新步骤中，以加速全局收敛。我们还建立了动量联邦学习的全局收敛性质，并对其收敛速度进行了上界分析，并与仅使用一阶梯度下降的联邦学习进行了比较。通过使用 MNIST 数据集进行实验，我们评估了 MFL 在不同机器学习模型下的收敛性能，并发现 MFL 比 FL 在全局收敛上有显著的改进。