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In this work we focus our attention on distributed optimization problems inthe context where the communication time between the server and the workers isnon-negligible. We obtain novel methods supporting bidirectional compression(both from the server to the workers and vice versa) that enjoy newstate-of-the-art theoretical communication complexity for convex and nonconvexproblems. Our bounds are the first that manage to decouple the variance/errorcoming from the workers-to-server and server-to-workers compression,transforming a multiplicative dependence to an additive one. Moreover, in theconvex regime, we obtain the first bounds that match the theoreticalcommunication complexity of gradient descent. Even in this convex regime, ouralgorithms work with biased gradient estimators, which is non-standard andrequires new proof techniques that may be of independent interest. Finally, ourtheoretical results are corroborated through suitable experiments.

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