Asynchronous decentralized accelerated stochastic gradient descent

In this work, we introduce an asynchronous decentralized accelerated stochastic gradient descent type of method for decentralized stochastic optimization, considering communication and synchronization are the major bottlenecks. We establish $\mathcal{O}(1/\epsilon)$ (resp., $\mathcal{O}(1/\sqrt{\epsilon})$) communication complexity and $\mathcal{O}(1/\epsilon^2)$ (resp., $\mathcal{O}(1/\epsilon)$) sampling complexity for solving general convex (resp., strongly convex) problems

An Accelerated Decentralized Stochastic Proximal Algorithm for Finite Sums

Modern large-scale finite-sum optimization relies on two key aspects: distribution and stochastic updates. For smooth and strongly convex problems, existing decentralized algorithms are slower than modern accelerated variance-reduced stochastic algorithms when run on a single machine, and are therefore not efficient. Centralized algorithms are fast, but their scaling is limited by global aggregation steps that result in communication bottlenecks. In this work, we propose an efficient \textbf{A}ccelerated \textbf{D}ecentralized stochastic algorithm for \textbf{F}inite \textbf{S}ums named ADFS, which uses local stochastic proximal updates and randomized pairwise communications between nodes. On $n$ machines, ADFS learns from $nm$ samples in the same time it takes optimal algorithms to learn from $m$ samples on one machine. This scaling holds until a critical network size is reached, which depends on communication delays, on the number of samples $m$, and on the network topology. We provide a theoretical analysis based on a novel augmented graph approach combined with a precise evaluation of synchronization times and an extension of the accelerated proximal coordinate gradient algorithm to arbitrary sampling. We illustrate the improvement of ADFS over state-of-the-art decentralized approaches with experiments.Comment: Code available in source files. arXiv admin note: substantial text overlap with arXiv:1901.0986

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