Stochastic Distributed Optimization under Average Second-order Similarity: Algorithms and Analysis
Dachao Lin, Yuze Han, Haishan Ye, Zhihua Zhang
Abstract
We study finite-sum distributed optimization problems involving a master node and $n-1$ local nodes under the popular $\delta$-similarity and $\mu$-strong convexity conditions. We propose two new algorithms, SVRS and AccSVRS, motivated by previous works. The non-accelerated SVRS method combines the techniques of gradient sliding and variance reduction and achieves a better communication complexity of $\tilde{\mathcal{O}}(n {+} \sqrt{n}\delta/\mu)$ compared to existing non-accelerated algorithms. Applying the framework proposed in Katyusha X, we also develop a directly accelerated version named AccSVRS with the $\tilde{\mathcal{O}}(n {+} n^{3/4}\sqrt{\delta/\mu})$ communication complexity. In contrast to existing results, our complexity bounds are entirely smoothness-free and exhibit superiority in ill-conditioned cases. Furthermore, we establish a nearly matched lower bound to verify the tightness of our AccSVRS method.
BibTeX
@inproceedings{
lin2023stochastic,
title={Stochastic Distributed Optimization under Average Second-order Similarity: Algorithms and Analysis},
author={Dachao Lin and Yuze Han and Haishan Ye and Zhihua Zhang},
booktitle={Thirty-seventh Conference on Neural Information Processing Systems},
year={2023},
url={https://openreview.net/forum?id=x5JCDCvR4b}
}