Federated Learning (FL) is a distributed machine learning approach that enables model training in communication efficient and privacy-preserving manner. The standard optimization method in FL is Federated Averaging (FedAvg), which performs multiple local SGD steps between communication rounds. FedAvg has been considered to lack algorithm adaptivity compared to modern first-order adaptive optimizations. In this paper, we propose new communication-efficient FL algortithms based on two adaptive frameworks: local adaptivity (PreFed) and server-side adaptivity (PreFedOp). Proposed methods adopt adaptivity by using a novel covariance matrix preconditioner. Theoretically, we provide convergence guarantees for our algorithms. The empirical experiments show our methods achieve state-of-the-art performances on both i.i.d. and non-i.i.d. settings.

Recent years have witnessed the growth of large-scale distributed machine learning algorithms -- specifically designed to accelerate model training by distributing computation across multiple machines. When scaling distributed training in this way, the communication overhead is often the bottleneck. In this paper, we study the local distributed Stochastic Gradient Descent~(SGD) algorithm, which reduces the communication overhead by decreasing the frequency of synchronization. While SGD with adaptive learning rates is a widely adopted strategy for training neural networks, it remains unknown how to implement adaptive learning rates in local SGD. To this end, we propose a novel SGD variant with reduced communication and adaptive learning rates, with provable convergence. Empirical results show that the proposed algorithm has fast convergence and efficiently reduces the communication overhead.