In the era of big data, optimizing large scale machine learning problems becomes a challenging task and draws significant attention. Asynchronous optimization algorithms come out as a promising solution. Recently, decoupled asynchronous proximal stochastic gradient descent (DAP-SGD) is proposed to minimize a composite function. It is claimed to be able to off-loads the computation bottleneck from server to workers by allowing workers to evaluate the proximal operators, therefore, server just need to do element-wise operations. However, it still suffers from slow convergence rate because of the variance of stochastic gradient is nonzero. In this paper, we propose a faster method, decoupled asynchronous proximal stochastic variance reduced gradient descent method (DAP-SVRG). We prove that our method has linear convergence for strongly convex problem. Large-scale experiments are also conducted in this paper, and results demonstrate our theoretical analysis.
University of Science and Technology of China（中国科学技术大学）
Asynchronous parallel optimization algorithms for solving large-scale machine learning problems have drawn significant attention from academia to industry recently. This paper proposes a novel algorithm, decoupled asynchronous proximal stochastic gradient descent (DAP-SGD), to minimize an objective function that is the composite of the average of multiple empirical losses and a regularization term. Unlike the traditional asynchronous proximal stochastic gradient descent (TAP-SGD) in which the master carries much of the computation load, the proposed algorithm off-loads the majority of computat…
Peking University（北京大学）；Microsoft Research（微软研究院）；Fudan University（复旦大学）；Academy of Mathematics and Systems Science, Chinese Academy of Sciences（中国科学院数学与系统科学研究院）
Regularized empirical risk minimization (R-ERM) is an important branch of machine learning, since it constrains the capacity of the hypothesis space and guarantees the generalization ability of the learning algorithm. Two classic proximal optimization algorithms, i.e., proximal stochastic gradient descent (ProxSGD) and proximal stochastic coordinate descent (ProxSCD) have been widely used to solve the R-ERM problem. Recently, variance reduction technique was proposed to improve ProxSGD and ProxSCD, and the corresponding ProxSVRG and ProxSVRCD have better convergence rate. These proximal algori…
University of Alberta（阿尔伯塔大学）；Wuhan University（武汉大学）
We study stochastic algorithms for solving nonconvex optimization problems with a convex yet possibly nonsmooth regularizer, which find wide applications in many practical machine learning applications. However, compared to asynchronous parallel stochastic gradient descent (AsynSGD), an algorithm targeting smooth optimization, the understanding of the behavior of stochastic algorithms for nonsmooth regularized optimization problems is limited, especially when the objective function is nonconvex. To fill this theoretical gap, in this paper, we propose and analyze asynchronous parallel stochasti…
Nonconvex and nonsmooth problems have recently attracted considerable attention in machine learning. However, developing efficient methods for the nonconvex and nonsmooth optimization problems with certain performance guarantee remains a challenge. Proximal coordinate descent (PCD) has been widely used for solving optimization problems, but the knowledge of PCD methods in the nonconvex setting is very limited. On the other hand, the asynchronous proximal coordinate descent (APCD) recently have received much attention in order to solve large-scale problems. However, the accelerated variants of …
Large models are prevalent in modern machine learning scenarios, including deep learning, recommender systems, etc., which can have millions or even billions of parameters. Parallel algorithms have become an essential solution technique to many large-scale machine learning jobs. In this paper, we propose a model parallel proximal stochastic gradient algorithm, AsyB-ProxSGD, to deal with large models using model parallel blockwise updates while in the meantime handling a large amount of training data using proximal stochastic gradient descent (ProxSGD). In our algorithm, worker nodes communicat…
KTH Royal Institute of Technology（KTH皇家理工学院）；Stockholm University（斯德哥尔摩大学）；ABB Corporate Research（ABB企业研究院）
In scalable machine learning systems, model training is often parallelized over multiple nodes that run without tight synchronization. Most analysis results for the related asynchronous algorithms use an upper bound on the information delays in the system to determine learning rates. Not only are such bounds hard to obtain in advance, but they also result in unnecessarily slow convergence. In this paper, we show that it is possible to use learning rates that depend on the actual time-varying delays in the system. We develop general convergence results for delay-adaptive asynchronous iterations…
Indian Institute of Technology Kanpur（印度理工学院坎普尔分校）；Radisys India Pvt. Ltd.（瑞迪斯印度私人有限公司）
We consider stochastic optimization of a smooth non-convex loss function with a convex non-smooth regularizer. In the online setting, where a single sample of the stochastic gradient of the loss is available at every iteration, the problem can be solved using the proximal stochastic gradient descent (SGD) algorithm and its variants. However in many problems, especially those arising in communications and signal processing, information beyond the stochastic gradient may be available thanks to the structure of the loss function. Such extra-gradient information is not used by SGD, but has been sh…
École normale supérieure（巴黎高等师范学院）；CNRS（法国国家科学研究中心）；PSL Research University（巴黎文理研究大学）；INRIA（法国国家信息与自动化研究所）；ENS（巴黎高等师范学院）；MILA（蒙特利尔学习算法研究所）；DIRO（蒙特利尔大学计算机科学与运筹学系）；Université de Montréal（蒙特利尔大学）
Due to their simplicity and excellent performance, parallel asynchronous variants of stochastic gradient descent have become popular methods to solve a wide range of large-scale optimization problems on multi-core architectures. Yet, despite their practical success, support for nonsmooth objectives is still lacking, making them unsuitable for many problems of interest in machine learning, such as the Lasso, group Lasso or empirical risk minimization with convex constraints. In this work, we propose and analyze ProxASAGA, a fully asynchronous sparse method inspired by SAGA, a variance reduced i…
A commonly cited inefficiency of neural network training using back-propagation is the update locking problem: each layer must wait for the signal to propagate through the full network before updating. Several alternatives that can alleviate this issue have been proposed. In this context, we consider a simple alternative based on minimal feedback, which we call Decoupled Greedy Learning (DGL). It is based on a classic greedy relaxation of the joint training objective, recently shown to be effective in the context of Convolutional Neural Networks (CNNs) on large-scale image classification. We c…
Decoupled learning is a branch of model parallelism which parallelizes the training of a network by splitting it depth-wise into multiple modules. Techniques from decoupled learning usually lead to stale gradient effect because of their asynchronous implementation, thereby causing performance degradation. In this paper, we propose an accumulated decoupled learning (ADL) which incorporates the gradient accumulation technique to mitigate the stale gradient effect. We give both theoretical and empirical evidences regarding how the gradient staleness can be reduced. We prove that the proposed meth…
Training directed neural networks typically requires forward-propagating data through a computation graph, followed by backpropagating error signal, to produce weight updates. All layers, or more generally, modules, of the network are therefore locked, in the sense that they must wait for the remainder of the network to execute forwards and propagate error backwards before they can be updated. In this work we break this constraint by decoupling modules by introducing a model of the future computation of the network graph. These models predict what the result of the modelled subgraph will produ…
When training neural networks, the use of Synthetic Gradients (SG) allows layers or modules to be trained without update locking - without waiting for a true error gradient to be backpropagated - resulting in Decoupled Neural Interfaces (DNIs). This unlocked ability of being able to update parts of a neural network asynchronously and with only local information was demonstrated to work empirically in Jaderberg et al (2016). However, there has been very little demonstration of what changes DNIs and SGs impose from a functional, representational, and learning dynamics point of view. In this pape…
Artifical Neural Networks are a particular class of learning systems modeled after biological neural functions with an interesting penchant for Hebbian learning, that is "neurons that wire together, fire together". However, unlike their natural counterparts, artificial neural networks have a close and stringent coupling between the modules of neurons in the network. This coupling or locking imposes upon the network a strict and inflexible structure that prevent layers in the network from updating their weights until a full feed-forward and backward pass has occurred. Such a constraint though m…
