  Federated Learning (FL) has emerged as the state-of-the-art approach for
learning from decentralized data in privacy-constrained scenarios. However,
system and statistical challenges hinder real-world applications, which demand
efficient learning from edge devices and robustness to heterogeneity. Despite
significant research efforts, existing approaches (i) are not sufficiently
robust, (ii) do not perform well in large-scale scenarios, and (iii) are not
communication efficient. In this work, we propose a novel Generalized
Heavy-Ball Momentum (GHBM), motivating its principled application to counteract
the effects of statistical heterogeneity in FL. Then, we present FedHBM as an
adaptive, communication-efficient by-design instance of GHBM. Extensive
experimentation on vision and language tasks, in both controlled and realistic
large-scale scenarios, provides compelling evidence of substantial and
consistent performance gains over the state of the art.
