  Decentralized federated learning (DFL) is a variant of federated learning,
where edge nodes only communicate with their one-hop neighbors to learn the
optimal model. However, as information exchange is restricted in a range of
one-hop in DFL, inefficient information exchange leads to more communication
rounds to reach the targeted training loss. This greatly reduces the
communication efficiency. In this paper, we propose a new non-uniform
quantization of model parameters to improve DFL convergence. Specifically, we
apply the Lloyd-Max algorithm to DFL (LM-DFL) first to minimize the
quantization distortion by adjusting the quantization levels adaptively.
Convergence guarantee of LM-DFL is established without convex loss assumption.
Based on LM-DFL, we then propose a new doubly-adaptive DFL, which jointly
considers the ascending number of quantization levels to reduce the amount of
communicated information in the training and adapts the quantization levels for
non-uniform gradient distributions. Experiment results based on MNIST and
CIFAR-10 datasets illustrate the superiority of LM-DFL with the optimal
quantized distortion and show that doubly-adaptive DFL can greatly improve
communication efficiency.
