Federated learning often suffers from unstable and slow convergence due to heterogeneous characteristics of participating clients. Such tendency is aggravated when the client participation ratio is low since the information collected from the clients at each round is prone to be more inconsistent. To tackle the challenge, we propose a novel federated learning framework, which improves the stability of the server-side aggregation step, which is achieved by sending the clients an accelerated model estimated with the global gradient to guide the local gradient updates. Our algorithm naturally aggregates and conveys the global update information to participants with no additional communication cost and does not require to store the past models in the clients. We also regularize local update to further reduce the bias and improve the stability of local updates. We perform comprehensive empirical studies on real data under various settings and demonstrate the remarkable performance of the proposed method in terms of accuracy and communication-efficiency compared to the stateof-the-art methods, especially with low client participation rates. Our code is available at https://github.com/ ninigapa0/FedAGM
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