Understanding Model Averaging in Federated Learning on Heterogeneous Data

Model averaging, a widely adopted technique in federated learning (FL), aggregates multiple client models trained on heterogeneous data to obtain a well-performed global model. However, the rationale behind its success is not well understood. To shed light on this issue, we investigate the geometric properties of model averaging by visualizing the loss/error landscape. The geometrical visualization shows that the client models surround the global model within a common basin, and the global model may deviate from the bottom of the basin even though it performs better than the client models. To further understand this phenomenon, we decompose the expected prediction error of the global model into five factors related to client models. Specifically, we find that the global-model error after early training mainly comes from i) the client-model error on non-overlapping data between client datasets and the global dataset and ii) the maximal distance between the global and client models. Inspired by these findings, we propose adopting iterative moving averaging (IMA) on global models to reduce the prediction error and limiting client exploration to control the maximal distance at the late training. Our experiments demonstrate that IMA significantly improves the accuracy and training speed of existing FL methods on benchmark datasets with various data heterogeneity.