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

TL;DR

This paper introduces new methods for distributed optimization with bidirectional compression that achieve state-of-the-art communication complexity bounds, even with biased gradient estimators, improving efficiency in non-negligible communication scenarios.

Contribution

The authors develop novel algorithms supporting bidirectional compression with decoupled variance bounds, matching gradient descent complexity in convex cases, and handle biased estimators with new proof techniques.

Findings

Achieved state-of-the-art theoretical communication complexity bounds.

Decoupled variance/error bounds for bidirectional compression.

Validated results through experiments.

Abstract

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.