  Distributed Stein Variational Gradient Descent (DSVGD) is a non-parametric
distributed learning framework for federated Bayesian learning, where multiple
clients jointly train a machine learning model by communicating a number of
non-random and interacting particles with the server. Since communication
resources are limited, selecting the clients with most informative local
learning updates can improve the model convergence and communication
efficiency. In this paper, we propose two selection schemes for DSVGD based on
Kernelized Stein Discrepancy (KSD) and Hilbert Inner Product (HIP). We derive
the upper bound on the decrease of the global free energy per iteration for
both schemes, which is then minimized to speed up the model convergence. We
evaluate and compare our schemes with conventional schemes in terms of model
accuracy, convergence speed, and stability using various learning tasks and
datasets.
