  Communication efficiency arises as a necessity in federated learning due to
limited communication bandwidth. To this end, the present paper develops an
algorithmic framework where an ensemble of pre-trained models is learned. At
each learning round, the server selects a subset of pre-trained models to
construct the ensemble model based on the structure of a graph, which
characterizes the server's confidence in the models. Then only the selected
models are transmitted to the clients, such that certain budget constraints are
not violated. Upon receiving updates from the clients, the server refines the
structure of the graph accordingly. The proposed algorithm is proved to enjoy
sub-linear regret bound. Experiments on real datasets demonstrate the
effectiveness of our novel approach.
