Sparse-SignSGD with Majority Vote for Communication-Efficient Distributed Learning

The training efficiency of complex deep learning models can be significantly improved through the use of distributed optimization. However, this process is often hindered by a large amount of communication cost between workers and a parameter server during iterations. To address this bottleneck, in this paper, we present a new communication-efficient algorithm that offers the synergistic benefits of both sparsification and sign quantization, called ${\sf S}^3$GD-MV. The workers in ${\sf S}^3$GD-MV select the top-$K$ magnitude components of their local gradient vector and only send the signs of these components to the server. The server then aggregates the signs and returns the results via a majority vote rule. Our analysis shows that, under certain mild conditions, ${\sf S}^3$GD-MV can converge at the same rate as signSGD while significantly reducing communication costs, if the sparsification parameter $K$ is properly chosen based on the number of workers and the size of the deep learning model. Experimental results using both independent and identically distributed (IID) and non-IID datasets demonstrate that the ${\sf S}^3$GD-MV attains higher accuracy than signSGD, significantly reducing communication costs. These findings highlight the potential of ${\sf S}^3$GD-MV as a promising solution for communication-efficient distributed optimization in deep learning.Comment: 13 pages, 7 figure

Natural Compression for Distributed Deep Learning

Modern deep learning models are often trained in parallel over a collection of distributed machines to reduce training time. In such settings, communication of model updates among machines becomes a significant performance bottleneck and various lossy update compression techniques have been proposed to alleviate this problem. In this work, we introduce a new, simple yet theoretically and practically effective compression technique: {\em natural compression (NC)}. Our technique is applied individually to all entries of the to-be-compressed update vector and works by randomized rounding to the nearest (negative or positive) power of two, which can be computed in a "natural" way by ignoring the mantissa. We show that compared to no compression, NC increases the second moment of the compressed vector by not more than the tiny factor \nicefrac{9}{8}, which means that the effect of NC on the convergence speed of popular training algorithms, such as distributed SGD, is negligible. However, the communications savings enabled by NC are substantial, leading to {\em $3$-$4\times$ improvement in overall theoretical running time}. For applications requiring more aggressive compression, we generalize NC to {\em natural dithering}, which we prove is {\em exponentially better} than the common random dithering technique. Our compression operators can be used on their own or in combination with existing operators for a more aggressive combined effect, and offer new state-of-the-art both in theory and practice.Comment: 8 pages, 20 pages of Appendix, 6 Tables, 14 Figure

The Convergence of Sparsified Gradient Methods

Distributed training of massive machine learning models, in particular deep neural networks, via Stochastic Gradient Descent (SGD) is becoming commonplace. Several families of communication-reduction methods, such as quantization, large-batch methods, and gradient sparsification, have been proposed. To date, gradient sparsification methods - where each node sorts gradients by magnitude, and only communicates a subset of the components, accumulating the rest locally - are known to yield some of the largest practical gains. Such methods can reduce the amount of communication per step by up to three orders of magnitude, while preserving model accuracy. Yet, this family of methods currently has no theoretical justification. This is the question we address in this paper. We prove that, under analytic assumptions, sparsifying gradients by magnitude with local error correction provides convergence guarantees, for both convex and non-convex smooth objectives, for data-parallel SGD. The main insight is that sparsification methods implicitly maintain bounds on the maximum impact of stale updates, thanks to selection by magnitude. Our analysis and empirical validation also reveal that these methods do require analytical conditions to converge well, justifying existing heuristics.Comment: NIPS 2018 - Advances in Neural Information Processing Systems; Authors in alphabetic orde