  Federated learning uses a set of techniques to efficiently distribute the
training of a machine learning algorithm across several devices, who own the
training data. These techniques critically rely on reducing the communication
cost -- the main bottleneck -- between the devices and a central server.
Federated learning algorithms usually take an optimization approach: they are
algorithms for minimizing the training loss subject to communication (and
other) constraints. In this work, we instead take a Bayesian approach for the
training task, and propose a communication-efficient variant of the Langevin
algorithm to sample a posteriori. The latter approach is more robust and
provides more knowledge of the \textit{a posteriori} distribution than its
optimization counterpart. We analyze our algorithm without assuming that the
target distribution is strongly log-concave. Instead, we assume the weaker log
Sobolev inequality, which allows for nonconvexity.

Machine Learning