A Novel Framework for the Analysis and Design of Heterogeneous Federated Learning

In federated learning, heterogeneity in the clients' local datasets and computation speeds results in large variations in the number of local updates performed by each client in each communication round. Naive weighted aggregation of such models causes objective inconsistency, that is, the global model converges to a stationary point of a mismatched objective function which can be arbitrarily different from the true objective. This paper provides a general framework to analyze the convergence of federated optimization algorithms with heterogeneous local training progress at clients. The analyses are conducted for both smooth non-convex and strongly convex settings, and can also be extended to partial client participation case. Additionally, it subsumes previously proposed methods such as FedAvg and FedProx, and provides the first principled understanding of the solution bias and the convergence slowdown due to objective inconsistency. Using insights from this analysis, we propose FedNova, a normalized averaging method that eliminates objective inconsistency while preserving fast error convergence.