EF21-P and Friends: Improved Theoretical Communication Complexity for Distributed Optimization with Bidirectional Compression

In this work we focus our attention on distributed optimization problems in the context where the communication time between the server and the workers is non-negligible. We obtain novel methods supporting bidirectional compression (both from the server to the workers and vice versa) that enjoy new state-of-the-art theoretical communication complexity for convex and nonconvex problems. Our bounds are the first that manage to decouple the variance/error coming from the workers-to-server and server-to-workers compression, transforming a multiplicative dependence to an additive one. Moreover, in the convex regime, we obtain the first bounds that match the theoretical communication complexity of gradient descent. Even in this convex regime, our algorithms work with biased gradient estimators, which is non-standard and requires new proof techniques that may be of independent interest. Finally, our theoretical results are corroborated through suitable experiments. Distributed Optimization and Bidirectional Compression In this paper, we consider distributed optimization problems in strongly convex, convex and nonconvex settings. Such problems arise in federated learning (Konečný et al., 2016; McMahan et al., 2017) and in deep learning (Ramesh et al., 2021). In federated learning, a large number of workers/devices/nodes contain local data and communicate with a parameter-server that performs optimization of a function * The work of Kaja Gruntkowska was performed during a Summer research internship in the Optimization and Machine Learning Lab at KAUST led by