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

A Discussion on Parallelization Schemes for Stochastic Vector Quantization Algorithms

This paper studies parallelization schemes for stochastic Vector Quantization algorithms in order to obtain time speed-ups using distributed resources. We show that the most intuitive parallelization scheme does not lead to better performances than the sequential algorithm. Another distributed scheme is therefore introduced which obtains the expected speed-ups. Then, it is improved to fit implementation on distributed architectures where communications are slow and inter-machines synchronization too costly. The schemes are tested with simulated distributed architectures and, for the last one, with Microsoft Windows Azure platform obtaining speed-ups up to 32 Virtual Machines

Robust and Communication-Efficient Collaborative Learning

We consider a decentralized learning problem, where a set of computing nodes aim at solving a non-convex optimization problem collaboratively. It is well-known that decentralized optimization schemes face two major system bottlenecks: stragglers' delay and communication overhead. In this paper, we tackle these bottlenecks by proposing a novel decentralized and gradient-based optimization algorithm named as QuanTimed-DSGD. Our algorithm stands on two main ideas: (i) we impose a deadline on the local gradient computations of each node at each iteration of the algorithm, and (ii) the nodes exchange quantized versions of their local models. The first idea robustifies to straggling nodes and the second alleviates communication efficiency. The key technical contribution of our work is to prove that with non-vanishing noises for quantization and stochastic gradients, the proposed method exactly converges to the global optimal for convex loss functions, and finds a first-order stationary point in non-convex scenarios. Our numerical evaluations of the QuanTimed-DSGD on training benchmark datasets, MNIST and CIFAR-10, demonstrate speedups of up to 3x in run-time, compared to state-of-the-art decentralized optimization methods