@inproceedings{
li2023detcgd,
title={Det-{CGD}: Compressed Gradient Descent with Matrix Stepsizes for Non-Convex Optimization},
author={Hanmin Li and Avetik Karagulyan and Peter Richt{\'a}rik},
booktitle={OPT 2023: Optimization for Machine Learning},
year={2023},
url={https://openreview.net/forum?id=zqE54pQRGn}
}
This paper introduces a new method for minimizing matrix-smooth non-convex objectives through the use of novel Compressed Gradient Descent (CGD) algorithms enhanced with a matrix-valued stepsize. The proposed algorithms are theoretically analyzed first in the single-node and subsequently in the distributed settings. Our theoretical results reveal that the matrix stepsize in CGD can capture the objective’s structure and lead to faster convergence compared to a scalar stepsize. As a byproduct of our general results, we emphasize the importance of selecting the compression mechanism and the matrix stepsize in a layer-wise manner, taking advantage of model structure. Moreover, we provide theoretical guarantees for free compression, by designing specific layer-wise compressors for the non-convex matrix smooth objectives. Our findings are supported with empirical evidence.
Det-CGD: Compressed Gradient Descent with Matrix Stepsizes for Non-Convex Optimization
Hanmin Li Avetik Karagulyan Peter Richtárik