  Traditional deep learning models are trained at a centralized server using
labeled data samples collected from end devices or users. Such data samples
often include private information, which the users may not be willing to share.
Federated learning (FL) is an emerging approach to train such learning models
without requiring the users to share their possibly private labeled data. In
FL, each user trains its copy of the learning model locally. The server then
collects the individual updates and aggregates them into a global model. A
major challenge that arises in this method is the need of each user to
efficiently transmit its learned model over the throughput limited uplink
channel. In this work, we tackle this challenge using tools from quantization
theory. In particular, we identify the unique characteristics associated with
conveying trained models over rate-constrained channels, and propose a suitable
quantization scheme for such settings, referred to as universal vector
quantization for FL (UVeQFed). We show that combining universal vector
quantization methods with FL yields a decentralized training system in which
the compression of the trained models induces only a minimum distortion. We
then theoretically analyze the distortion, showing that it vanishes as the
number of users grows. We also characterize the convergence of models trained
with the traditional federated averaging method combined with UVeQFed to the
model which minimizes the loss function. Our numerical results demonstrate the
gains of UVeQFed over previously proposed methods in terms of both distortion
induced in quantization and accuracy of the resulting aggregated model.
