  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.
