MATCHA: Speeding Up Decentralized SGD via Matching Decomposition Sampling

TL;DR

MATCHA is a novel algorithm that decomposes network topologies into matchings to optimize the error-runtime trade-off in decentralized SGD, achieving faster training times across various networks and datasets.

Contribution

The paper introduces MATCHA, a new method that efficiently balances communication and error convergence in decentralized training by topology decomposition.

Findings

MATCHA reduces training time by up to 5x compared to vanilla decentralized SGD.

Theoretical analysis confirms MATCHA's optimal error-runtime trade-off.

Experimental results across multiple datasets validate the effectiveness of MATCHA.

Abstract

This paper studies the problem of error-runtime trade-off, typically encountered in decentralized training based on stochastic gradient descent (SGD) using a given network. While a denser (sparser) network topology results in faster (slower) error convergence in terms of iterations, it incurs more (less) communication time/delay per iteration. In this paper, we propose MATCHA, an algorithm that can achieve a win-win in this error-runtime trade-off for any arbitrary network topology. The main idea of MATCHA is to parallelize inter-node communication by decomposing the topology into matchings. To preserve fast error convergence speed, it identifies and communicates more frequently over critical links, and saves communication time by using other links less frequently. Experiments on a suite of datasets and deep neural networks validate the theoretical analyses and demonstrate that MATCHA takes up to $5\times$ less time than vanilla decentralized SGD to reach the same training loss.