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This paper studies the problem of error-runtime trade-off, typicallyencountered in decentralized training based on stochastic gradient descent(SGD) using a given network. While a denser (sparser) network topology resultsin faster (slower) error convergence in terms of iterations, it incurs more(less) communication time/delay per iteration. In this paper, we proposeMATCHA, an algorithm that can achieve a win-win in this error-runtime trade-offfor any arbitrary network topology. The main idea of MATCHA is to parallelizeinter-node communication by decomposing the topology into matchings. Topreserve fast error convergence speed, it identifies and communicates morefrequently over critical links, and saves communication time by using otherlinks less frequently. Experiments on a suite of datasets and deep neuralnetworks validate the theoretical analyses and demonstrate that MATCHA takes upto $5\times$ less time than vanilla decentralized SGD to reach the sametraining loss.

MATCHA: Speeding Up Decentralized SGD via Matching Decomposition Sampling