We develop and analyze MARINA: a new communication efficient method for non-convex distributed learning over heterogeneous datasets. MARINA employs a novel communication compression strategy based on the compression of gradient differences which is reminiscent of but different from the strategy employed in the DIANA method of . Unlike virtually all competing distributed first-order methods, including DIANA, ours is based on a carefully designed biased gradient estimator, which is the key to its superior theoretical and practical performance. To the best of our knowledge, the communication complexity bounds we prove for MARINA are strictly superior to those of all previous first order methods. Further, we develop and analyze two variants of MARINA: VR-MARINA and PP-MARINA. The first method is designed for the case when the local loss functions owned by clients are either of a finite sum or of an expectation form, and the second method allows for partial participation of clients -a feature important in federated learning. All our methods are superior to previous state-of-theart methods in terms of the oracle/communication complexity. Finally, we provide convergence analysis of all methods for problems satisfying the Polyak-Lojasiewicz condition.

Federated Learning (FL) has emerged as a promising technique for edge devices to collaboratively learn a shared machine learning model while keeping training data locally on the device, thereby removing the need to store and access the full data in the cloud. However, FL is difficult to implement, test and deploy in practice considering heterogeneity in common edge device settings, making it fundamentally hard for researchers to efficiently prototype and test their optimization algorithms. In this work, our aim is to alleviate this problem by introducing FL_PyTorch : a suite of opensource software written in python that builds on top of one the most popular research Deep Learning (DL) framework PyTorch. We built FL_PyTorch as a research simulator for FL to enable fast development, prototyping and experimenting with new and existing FL optimization algorithms. Our system supports abstractions that provide researchers with a sufficient level of flexibility to experiment with existing and novel approaches to advance the state-of-theart. Furthermore, FL_PyTorch is a simple to use console system, allows to run several clients simultaneously using local CPUs or GPU(s), and even remote compute devices without the need for any distributed implementation provided by the user. FL_PyTorch also offers a Graphical User Interface. For new methods, researchers only provide the centralized implementation of their algorithm. To showcase the possibilities and usefulness of our system, we experiment with several well-known state-of-the-art FL algorithms and a few of the most common FL datasets.

Due to the communication bottleneck in distributed and federated learning applications, algorithms using communication compression have attracted significant attention and are widely used in practice. Moreover, there exists client-variance in federated learning due to the total number of heterogeneous clients is usually very large and the server is unable to communicate with all clients in each communication round. In this paper, we address these two issues together by proposing compressed and client-variance reduced methods. Concretely, we introduce COFIG and FRECON, which successfully enjoy communication compression with client-variance reduction. The total communication round of COFIG is O() in the nonconvex setting, where N is the total number of clients, S is the number of communicated clients in each round, ǫ is the convergence error, and ω is the parameter for the compression operator. Besides, our FRECON can converge faster than COFIG in the nonconvex setting, and it converges with O( (1+ω)) communication rounds. In the convex setting, COFIG converges within the communication rounds O( (1+ω)), which is also the first convergence result for compression schemes that do not communicate with all the clients in each round. In sum, both COFIG and FRECON do not need to communicate with all the clients and provide first/faster convergence results for convex and nonconvex federated learning, while previous works either require full clients communication (thus not practical) or obtain worse convergence results.