  Federated learning (FL) refers to the learning paradigm that trains machine
learning models directly in the decentralized systems consisting of smart edge
devices without transmitting the raw data, which avoids the heavy communication
costs and privacy concerns. Given the typical heterogeneous data distributions
in such situations, the popular FL algorithm \emph{Federated Averaging}
(FedAvg) suffers from weight divergence and thus cannot achieve a competitive
performance for the global model (denoted as the \emph{initial performance} in
FL) compared to centralized methods. In this paper, we propose the local
continual training strategy to address this problem. Importance weights are
evaluated on a small proxy dataset on the central server and then used to
constrain the local training. With this additional term, we alleviate the
weight divergence and continually integrate the knowledge on different local
clients into the global model, which ensures a better generalization ability.
Experiments on various FL settings demonstrate that our method significantly
improves the initial performance of federated models with few extra
communication costs.
