Distributed Fixed Point Methods with Compressed Iterates

TL;DR

This paper introduces the first distributed fixed point methods with compressed iterates, providing a theoretical framework and communication complexity bounds relevant for federated learning scenarios involving model compression.

Contribution

It develops the first fixed point and distributed methods with compressed iterates, along with analysis under natural assumptions, applicable to federated learning.

Findings

Established communication complexity bounds for the proposed methods

Developed variance reduced algorithms for fixed point problems

Provided theoretical analysis under natural assumptions

Abstract

We propose basic and natural assumptions under which iterative optimization methods with compressed iterates can be analyzed. This problem is motivated by the practice of federated learning, where a large model stored in the cloud is compressed before it is sent to a mobile device, which then proceeds with training based on local data. We develop standard and variance reduced methods, and establish communication complexity bounds. Our algorithms are the first distributed methods with compressed iterates, and the first fixed point methods with compressed iterates.