  Federated Learning (FL) has recently received a lot of attention for
large-scale privacy-preserving machine learning. However, high communication
overheads due to frequent gradient transmissions decelerate FL. To mitigate the
communication overheads, two main techniques have been studied: (i) local
update of weights characterizing the trade-off between communication and
computation and (ii) gradient compression characterizing the trade-off between
communication and precision. To the best of our knowledge, studying and
balancing those two trade-offs jointly and dynamically while considering their
impacts on convergence has remained unresolved even though it promises
significantly faster FL. In this paper, we first formulate our problem to
minimize learning error with respect to two variables: local update
coefficients and sparsity budgets of gradient compression who characterize
trade-offs between communication and computation/precision, respectively. We
then derive an upper bound of the learning error in a given wall-clock time
considering the interdependency between the two variables. Based on this
theoretical analysis, we propose an enhanced FL scheme, namely Fast FL (FFL),
that jointly and dynamically adjusts the two variables to minimize the learning
error. We demonstrate that FFL consistently achieves higher accuracies faster
than similar schemes existing in the literature.
