  Client-wise heterogeneity is one of the major issues that hinder effective
training in federated learning (FL). Since the data distribution on each client
may differ dramatically, the client selection strategy can largely influence
the convergence rate of the FL process. Several recent studies adopt active
client selection strategies. However, they neglect the loss correlations
between the clients and achieve marginal improvement compared to the uniform
selection strategy. In this work, we propose FedGP -- a federated learning
framework built on a correlation-based client selection strategy, to boost the
convergence rate of FL. Specifically, we first model the loss correlations
between the clients with a Gaussian Process (GP). To make the GP training
feasible in the communication-bounded FL process, we develop a GP training
method utilizing the historical samples efficiently to reduce the communication
cost. Finally, based on the correlations we learned, we derive the client
selection with an enlarged reduction of expected global loss in each round. Our
experimental results show that compared to the latest active client selection
strategy, FedGP can improve the convergence rates by $1.3\sim2.3\times$ and
$1.2\sim1.4\times$ on FMNIST and CIFAR-10, respectively.
