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Federated learning (FL) is an emerging learning paradigm to tackle massivelydistributed data. In Federated Learning, a set of clients jointly perform amachine learning task under the coordination of a server. The FedAvg algorithmis one of the most widely used methods to solve Federated Learning problems. InFedAvg, the learning rate is a constant rather than changing adaptively. Theadaptive gradient methods show superior performance over the constant learningrate schedule; however, there is still no general framework to incorporateadaptive gradient methods into the federated setting. In this paper, we propose\textbf{FedDA}, a novel framework for local adaptive gradient methods. Theframework adopts a restarted dual averaging technique and is flexible withvarious gradient estimation methods and adaptive learning rate formulations. Inparticular, we analyze \textbf{FedDA-MVR}, an instantiation of our framework,and show that it achieves gradient complexity $\tilde{O}(\epsilon^{-1.5})$ andcommunication complexity $\tilde{O}(\epsilon^{-1})$ for finding a stationarypoint $\epsilon$. This matches the best known rate for first-order FLalgorithms and \textbf{FedDA-MVR} is the first adaptive FL algorithm thatachieves this rate. We also perform extensive numerical experiments to verifythe efficacy of our method.

FedDA: Faster Framework of Local Adaptive Gradient Methods via Restarted Dual Averaging