  In federated learning (FL), a number of devices train their local models and
upload the corresponding parameters or gradients to the base station (BS) to
update the global model while protecting their data privacy. However, due to
the limited computation and communication resources, the number of local
trainings (a.k.a. local update) and that of aggregations (a.k.a. global update)
need to be carefully chosen. In this paper, we investigate and analyze the
optimal trade-off between the number of local trainings and that of global
aggregations to speed up the convergence and enhance the prediction accuracy
over the existing works. Our goal is to minimize the global loss function under
both the delay and the energy consumption constraints. In order to make the
optimization problem tractable, we derive a new and tight upper bound on the
loss function, which allows us to obtain closed-form expressions for the number
of local trainings and that of global aggregations. Simulation results show
that our proposed scheme can achieve a better performance in terms of the
prediction accuracy, and converge much faster than the baseline schemes.
