D-Cliques: Compensating for Data Heterogeneity with Topology in Decentralized Federated Learning

The convergence speed of machine learning models trained with Federated Learning is significantly affected by heterogeneous data partitions, even more so in a fully decentralized setting without a central server. In this paper, we show that the impact of label distribution skew, an important type of data heterogeneity, can be significantly reduced by carefully designing the underlying communication topology. We present D-Cliques, a novel topology that reduces gradient bias by grouping nodes in sparsely interconnected cliques such that the label distribution in a clique is representative of the global label distribution. We also show how to adapt the updates of decentralized SGD to obtain unbiased gradients and implement an effective momentum with D-Cliques. Our extensive empirical evaluation on MNIST and CIFAR10 validates our design and demonstrates that our approach achieves similar convergence speed as a fully-connected topology, while providing a significant reduction in the number of edges and messages. In a 1000-node topology, D-Cliques require 98% less edges and 96% less total messages, with further possible gains using a small-world topology across cliques.