This paper proposes adaptive federated optimization methods for federated learning (FL), including federated versions of ADAGRAD, ADAM, and YOGI. These methods are designed to address the challenges of client heterogeneity and communication efficiency in FL. The authors introduce a general framework for federated optimization that allows for the use of adaptive optimizers on both clients and servers. They show that this framework can significantly improve the performance of FL by incorporating adaptivity, which is often lacking in standard federated optimization methods like FEDAVG. The paper provides convergence analysis for these methods in non-convex settings and demonstrates their effectiveness through extensive experiments on various FL tasks. The results show that adaptive optimizers can achieve better convergence and performance, especially in cross-device FL settings where client data is highly heterogeneous. The study also highlights the importance of adaptivity in handling the challenges of FL, such as client drift and communication efficiency.This paper proposes adaptive federated optimization methods for federated learning (FL), including federated versions of ADAGRAD, ADAM, and YOGI. These methods are designed to address the challenges of client heterogeneity and communication efficiency in FL. The authors introduce a general framework for federated optimization that allows for the use of adaptive optimizers on both clients and servers. They show that this framework can significantly improve the performance of FL by incorporating adaptivity, which is often lacking in standard federated optimization methods like FEDAVG. The paper provides convergence analysis for these methods in non-convex settings and demonstrates their effectiveness through extensive experiments on various FL tasks. The results show that adaptive optimizers can achieve better convergence and performance, especially in cross-device FL settings where client data is highly heterogeneous. The study also highlights the importance of adaptivity in handling the challenges of FL, such as client drift and communication efficiency.