Paper Info
Title
Decentralized Stochastic Optimization and Gossip Algorithms with Compressed Communication.
Abstract
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 $omega leq 1$ ($omega=1$ meaning no compression). We (i) propose a novel gossip-based stochastic gradient descent algorithm, CHOCO-SGD, that converges at rate $mathcal{O}left(1/(nT) + 1/(T delta^2 omega)^2right)$ for strongly convex objectives, where $T$ denotes the number of iterations and $delta$ the eigengap of the connectivity matrix. Despite compression quality and network connectivity affecting the higher order terms, the first term in the rate, $mathcal{O}(1/(nT))$, 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 $mathcal{O}(1/(delta^2omega) log (1/epsilon))$ for accuracy $epsilon u003e 0$. This is (up to our knowledge) the first gossip algorithm that supports arbitrary compressed messages for $omega u003e 0$ 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.
Year
Venue
Field
2019
arXiv: Learning
Stochastic optimization,Gossip algorithms,Computer science,Theoretical computer science,Artificial intelligence,Machine learning
DocType
Volume
Citations 
Journal
abs/1902.00340
3
PageRank 
References 
Authors
0.36
27
3
Name
Order
Citations
PageRank
Anastasia Koloskova131.38
Sebastian U. Stich213516.54
Martin Jaggi385254.16