  Federated Learning (FL) has garnered increasing attention due to its unique
characteristic of allowing heterogeneous clients to process their private data
locally and interact with a central server, while being respectful of privacy.
A critical bottleneck in FL is the communication cost. A pivotal strategy to
mitigate this burden is \emph{Local Training}, which involves running multiple
local stochastic gradient descent iterations between communication phases. Our
work is inspired by the innovative \emph{Scaffnew} algorithm, which has
considerably advanced the reduction of communication complexity in FL. We
introduce FedComLoc (Federated Compressed and Local Training), integrating
practical and effective compression into \emph{Scaffnew} to further enhance
communication efficiency. Extensive experiments, using the popular TopK
compressor and quantization, demonstrate its prowess in substantially reducing
communication overheads in heterogeneous settings.
