267529
20190831134119.0
CONF
Decentralized Stochastic Optimization and Gossip Algorithms with Compressed Communication
2019-06-09
2019-06-09
Conference Papers
PMLR
We consider decentralized stochastic optimization with the objective function (e.g. data samples for machine learning task) being distributed over n machines that can only communicate to their neighbors on a fixed communication graph. To reduce the communication bottleneck, the nodes compress (e.g. quantize or sparsify) their model updates. We cover both unbiased and biased compression operators with quality denoted by \omega <= 1 (\omega=1 meaning no compression). We (i) propose a novel gossip-based stochastic gradient descent algorithm, CHOCO-SGD, that converges at rate O(1/(nT) + 1/(T \delta^2 \omega)^2) for strongly convex objectives, where T denotes the number of iterations and δ the eigengap of the connectivity matrix. Despite compression quality and network connectivity affecting the higher order terms, the first term in the rate, O(1/(nT)), is the same as for the centralized baseline with exact communication. We (ii) present a novel gossip algorithm, CHOCO-GOSSIP, for the average consensus problem that converges in time O(1/(\delta^2\omega) \log (1/\epsilon)) for accuracy \epsilon > 0. This is (up to our knowledge) the first gossip algorithm that supports arbitrary compressed messages for \omega > 0 and still exhibits linear convergence. We (iii) show in experiments that both of our algorithms do outperform the respective state-of-the-art baselines and CHOCO-SGD can reduce communication by at least two orders of magnitudes.
CC BY
ml-ai
260674
Koloskova, Anastasiia
289041
250586
Stich, Sebastian Urban
278401
250160
Jaggi, Martin
276449
ICML 2019 - International Conference on Machine Learning
Long Beach, California, USA
9-15 June 2019
ICML 2019 - International Conference on Machine Learning
97
martin.jaggi@epfl.ch
4981541
Final
http://infoscience.epfl.ch/record/267529/files/koloskova19a-supp.pdf
oai:infoscience.epfl.ch:267529
IC
conf
252581
jennifer.bachmann-ona@epfl.ch
martin.jaggi@epfl.ch
MLO
U13319
Grolimund, Raphael
anastasia.koloskova@epfl.ch
pierre.devaud@epfl.ch
EPFL
REVIEWED
CONF
overwrite