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

Understand

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.