On the Optimal Time Complexities in Decentralized Stochastic Asynchronous Optimization
Alexander Tyurin, Peter Richtárik
Abstract
We consider the decentralized stochastic asynchronous optimization setup, where many workers asynchronously calculate stochastic gradients and asynchronously communicate with each other using edges in a multigraph. For both homogeneous and heterogeneous setups, we prove new time complexity lower bounds under the assumption that computation and communication speeds are bounded by constants. After that, we developed a new nearly optimal method, Fragile SGD, and a new optimal method, Amelie SGD, that converge with arbitrary heterogeneous computation and communication speeds and match our lower bounds (up to a logarithmic factor in the homogeneous setting). Our time complexities are new, nearly optimal, and provably improve all previous asynchronous/synchronous stochastic methods in the decentralized setup.
BibTeX
@inproceedings{
tyurin2024on,
title={On the Optimal Time Complexities in Decentralized Stochastic Asynchronous Optimization},
author={Alexander Tyurin and Peter Richt{\'a}rik},
booktitle={The Thirty-eighth Annual Conference on Neural Information Processing Systems},
year={2024},
url={https://openreview.net/forum?id=IXRa8adMHX}
}