We design and implement a distributed multinode synchronous SGD algorithm, without altering hyper parameters, or compressing data, or altering algorithmic behavior. We perform a detailed analysis of scaling, and identify optimal design points for different networks. We demonstrate scaling of CNNs on 100s of nodes, and present what we believe to be record training throughputs. A 512 minibatch VGG-A CNN training run is scaled 90X on 128 nodes. Also 256 minibatch VGG-A and OverFeat-FAST networks are scaled 53X and 42X respectively on a 64 node cluster. We also demonstrate the generality of our approach via best-in-class 6.5X scaling for a 7-layer DNN on 16 nodes. Thereafter we attempt to democratize deep-learning by training on an Ethernet based AWS cluster and show ~14X scaling on 16 nodes.
Department of Engineering Sciences, University of Oxford（牛津大学工程科学系）；University of Oxford（牛津大学）
We introduce a new, high-throughput, synchronous, distributed, data-parallel, stochastic-gradient-descent learning algorithm. This algorithm uses amortized inference in a compute-cluster-specific, deep, generative, dynamical model to perform joint posterior predictive inference of the mini-batch gradient computation times of all worker-nodes in a parallel computing cluster. We show that a synchronous parameter server can, by utilizing such a model, choose an optimal cutoff time beyond which mini-batch gradient messages from slow workers are ignored that maximizes overall mini-batch gradient co…
Computer Laboratory, University of Cambridge（剑桥大学计算机实验室）
Most machine learning and deep neural network algorithms rely on certain iterative algorithms to optimise their utility/cost functions, e.g. Stochastic Gradient Descent. In distributed learning, the networked nodes have to work collaboratively to update the model parameters, and the way how they proceed is referred to as synchronous parallel design (or barrier control). Synchronous parallel protocol is the building block of any distributed learning framework, and its design has direct impact on the performance and scalability of the system. In this paper, we propose a new barrier control techn…
Distributed training of deep learning models on large-scale training data is typically conducted with asynchronous stochastic optimization to maximize the rate of updates, at the cost of additional noise introduced from asynchrony. In contrast, the synchronous approach is often thought to be impractical due to idle time wasted on waiting for straggling workers. We revisit these conventional beliefs in this paper, and examine the weaknesses of both approaches. We demonstrate that a third approach, synchronous optimization with backup workers, can avoid asynchronous noise while mitigating for th…
Distributed training of deep learning models on large-scale training data is typically conducted with asynchronous stochastic optimization to maximize the rate of updates, at the cost of additional noise introduced from asynchrony. In contrast, the synchronous approach is often thought to be impractical due to idle time wasted on waiting for straggling workers. We revisit these conventional beliefs in this paper, and examine the weaknesses of both approaches. We demonstrate that a third approach, synchronous optimization with backup workers, can avoid asynchronous noise while mitigating for th…
Asynchronous stochastic gradient descent (SGD) is attractive from a speed perspective because workers do not wait for synchronization. However, the Transformer model converges poorly with asynchronous SGD, resulting in substantially lower quality compared to synchronous SGD. To investigate why this is the case, we isolate differences between asynchronous and synchronous methods to investigate batch size and staleness effects. We find that summing several asynchronous updates, rather than applying them immediately, restores convergence behavior. With this hybrid method, Transformer training for…
Data parallelism has become the de facto standard for training Deep Neural Network on multiple processing units. In this work we propose DC-S3GD, a decentralized (without Parameter Server) stale-synchronous version of the Delay-Compensated Asynchronous Stochastic Gradient Descent (DC-ASGD) algorithm. In our approach, we allow for the overlap of computation and communication, and compensate the inherent error with a first-order correction of the gradients. We prove the effectiveness of our approach by training Convolutional Neural Network with large batches and achieving state-of-the-art result…
Communication overhead is the key challenge for distributed training. Gradient compression is a widely used approach to reduce communication traffic. When combining with parallel communication mechanism method like pipeline, gradient compression technique can greatly alleviate the impact of communication overhead. However, there exists two problems of gradient compression technique to be solved. Firstly, gradient compression brings in extra computation cost, which will delay the next training iteration. Secondly, gradient compression usually leads to the decrease of convergence accuracy.
Deep learning is a popular machine learning technique and has been applied to many real-world problems. However, training a deep neural network is very time-consuming, especially on big data. It has become difficult for a single machine to train a large model over large datasets. A popular solution is to distribute and parallelize the training process across multiple machines using the parameter server framework. In this paper, we present a distributed paradigm on the parameter server framework called Dynamic Stale Synchronous Parallel (DSSP) which improves the state-of-the-art Stale Synchrono…
A rich body of prior work has highlighted the existence of communication bottlenecks in synchronous data-parallel training. To alleviate these bottlenecks, a long line of recent work proposes gradient and model compression methods. In this work, we evaluate the efficacy of gradient compression methods and compare their scalability with optimized implementations of synchronous data-parallel SGD across more than 200 different setups. Surprisingly, we observe that only in 6 cases out of more than 200, gradient compression methods provide speedup over optimized synchronous data-parallel training i…
Imperial College London（帝国理工学院）；Microsoft Research（微软研究院）；Humboldt-Universität zu Berlin（柏林洪堡大学）
Deep learning models are trained on servers with many GPUs, and training must scale with the number of GPUs. Systems such as TensorFlow and Caffe2 train models with parallel synchronous stochastic gradient descent: they process a batch of training data at a time, partitioned across GPUs, and average the resulting partial gradients to obtain an updated global model. To fully utilise all GPUs, systems must increase the batch size, which hinders statistical efficiency. Users tune hyper-parameters such as the learning rate to compensate for this, which is complex and model-specific. We describe CR…
Stochastic Gradient Descent (SGD) is the most popular algorithm for training deep neural networks (DNNs). As larger networks and datasets cause longer training times, training on distributed systems is common and distributed SGD variants, mainly asynchronous and synchronous SGD, are widely used. Asynchronous SGD is communication efficient but suffers from accuracy degradation due to delayed parameter updating. Synchronous SGD becomes communication intensive when the number of nodes increases regardless of its advantage. To address these issues, we introduce Layered SGD (LSGD), a new decentrali…
Hong Kong Baptist University（香港浸会大学）；Shenzhen District Block Technology Co., Ltd.（深圳区块科技有限公司）
Distributed synchronous stochastic gradient descent (S-SGD) has been widely used in training large-scale deep neural networks (DNNs), but it typically requires very high communication bandwidth between computational workers (e.g., GPUs) to exchange gradients iteratively. Recently, Top-$k$ sparsification techniques have been proposed to reduce the volume of data to be exchanged among workers. Top-$k$ sparsification can zero-out a significant portion of gradients without impacting the model convergence. However, the sparse gradients should be transferred with their irregular indices, which makes…
There is an increased interest in building data analytics frameworks with advanced algebraic capabilities both in industry and academia. Many of these frameworks, e.g., TensorFlow and BIDMach, implement their compute-intensive primitives in two flavors---as multi-thread routines for multi-core CPUs and as highly-parallel kernels executed on GPU. Stochastic gradient descent (SGD) is the most popular optimization method for model training implemented extensively on modern data analytics platforms. While the data-intensive properties of SGD are well-known, there is an intense debate on which of t…
Penn State Behrend（宾夕法尼亚州立大学贝伦德分校）；University of California, Davis（加州大学戴维斯分校）；University of Iowa（爱荷华大学）
Due to the big size of data and limited data storage volume of a single computer or a single server, data are often stored in a distributed manner. Thus, performing large-scale machine learning operations with the distributed datasets through communication networks is often required. In this paper, we study the convergence rate of the distributed dual coordinate ascent for distributed machine learning problems in a general tree-structured network. Since a tree network model can be understood as the generalization of a star network model, our algorithm can be thought of as the generalization of…
Training time on large datasets for deep neural networks is the principal workflow bottleneck in a number of important applications of deep learning, such as object classification and detection in automatic driver assistance systems (ADAS). To minimize training time, the training of a deep neural network must be scaled beyond a single machine to as many machines as possible by distributing the optimization method used for training. While a number of approaches have been proposed for distributed stochastic gradient descent (SGD), at the current time synchronous approaches to distributed SGD app…
We make distributed stochastic gradient descent faster by exchanging sparse updates instead of dense updates. Gradient updates are positively skewed as most updates are near zero, so we map the 99% smallest updates (by absolute value) to zero then exchange sparse matrices. This method can be combined with quantization to further improve the compression. We explore different configurations and apply them to neural machine translation and MNIST image classification tasks. Most configurations work on MNIST, whereas different configurations reduce convergence rate on the more complex translation t…
Nonlinear conjugate gradient (NLCG) based optimizers have shown superior loss convergence properties compared to gradient descent based optimizers for traditional optimization problems. However, in Deep Neural Network (DNN) training, the dominant optimization algorithm of choice is still Stochastic Gradient Descent (SGD) and its variants. In this work, we propose and evaluate the stochastic preconditioned nonlinear conjugate gradient algorithm for large scale DNN training tasks. We show that a nonlinear conjugate gradient algorithm improves the convergence speed of DNN training, especially in …
IST Universidade de Lisboa（里斯本大学高等技术学院）；Institute for Systems and Robotics（系统与机器人研究所）
Real-world network applications must cope with failing nodes, malicious attacks, or nodes facing corrupted data - data classified as outliers. Our work addresses these concerns in the scope of the sensor network localization problem where, despite the abundance of technical literature, prior research seldom considered outlier data. We propose robust, fast, and distributed network localization algorithms, resilient to high-power noise, but also precise under regular Gaussian noise. We use a Huber M-estimator, thus obtaining a robust (but nonconvex) optimization problem. We convexify and change …
The Ohio State University（俄亥俄州立大学）；Iowa State University（爱荷华州立大学）
To increase the training speed of distributed learning, recent years have witnessed a significant amount of interest in developing both synchronous and asynchronous distributed stochastic variance-reduced optimization methods. However, all existing synchronous and asynchronous distributed training algorithms suffer from various limitations in either convergence speed or implementation complexity. This motivates us to propose an algorithm called STNTHESIS (semi-asynchronous path-integrated stochastic gradient search), which leverages the special structure of the variance-reduction framework to …
University of Illinois, Urbana-Champaign（伊利诺伊大学厄巴纳-香槟分校）
We present Zeno, a technique to make distributed machine learning, particularly Stochastic Gradient Descent (SGD), tolerant to an arbitrary number of faulty workers. Zeno generalizes previous results that assumed a majority of non-faulty nodes; we need assume only one non-faulty worker. Our key idea is to suspect workers that are potentially defective. Since this is likely to lead to false positives, we use a ranking-based preference mechanism. We prove the convergence of SGD for non-convex problems under these scenarios. Experimental results show that Zeno outperforms existing approaches.
Georgia Institute of Technology（佐治亚理工学院）；IBM Thomas J. Watson Research Center（IBM托马斯·J·沃森研究中心）
Despite their popularity, the practical performance of asynchronous stochastic gradient descent methods (ASGD) for solving large scale machine learning problems are not as good as theoretical results indicate. We adopt and analyze a synchronous K-step averaging stochastic gradient descent algorithm which we call K-AVG. We establish the convergence results of K-AVG for nonconvex objectives and explain why the K-step delay is necessary and leads to better performance than traditional parallel stochastic gradient descent which is a special case of K-AVG with $K=1$. We also show that K-AVG scales …
University of Maryland, College Park（马里兰大学帕克分校）；United States Naval Academy（美国海军学院）
Variance reduction (VR) methods boost the performance of stochastic gradient descent (SGD) by enabling the use of larger, constant stepsizes and preserving linear convergence rates. However, current variance reduced SGD methods require either high memory usage or an exact gradient computation (using the entire dataset) at the end of each epoch. This limits the use of VR methods in practical distributed settings. In this paper, we propose a variance reduction method, called VR-lite, that does not require full gradient computations or extra storage. We explore distributed synchronous and asynchr…
This work addresses distributed optimization, where a network of agents wants to minimize a global strongly convex objective function. The global function can be written as a sum of local convex functions, each of which is associated with an agent. We propose a continuous-time distributed mirror descent algorithm that uses purely local information to converge to the global optimum. Unlike previous work on distributed mirror descent, we incorporate an integral feedback in the update, allowing the algorithm to converge with a constant step-size when discretized. We establish the asymptotic conve…
Distributed asynchronous SGD has become widely used for deep learning in large-scale systems, but remains notorious for its instability when increasing the number of workers. In this work, we study the dynamics of distributed asynchronous SGD under the lens of Lagrangian mechanics. Using this description, we introduce the concept of energy to describe the optimization process and derive a sufficient condition ensuring its stability as long as the collective energy induced by the active workers remains below the energy of a target synchronous process. Making use of this criterion, we derive a s…
The training of modern deep learning neural network calls for large amounts of computation, which is often provided by GPUs or other specific accelerators. To scale out to achieve faster training speed, two update algorithms are mainly applied in the distributed training process, i.e. the Synchronous SGD algorithm (SSGD) and Asynchronous SGD algorithm (ASGD). SSGD obtains good convergence point while the training speed is slowed down by the synchronous barrier. ASGD has faster training speed but the convergence point is lower when compared to SSGD. To sufficiently utilize the advantages of SSG…
University of Rochester（罗切斯特大学）；IBM T. J. Watson Research Center（IBM T. J. 沃森研究中心）；ETH Zurich（苏黎世联邦理工学院）；Tencent AI Lab（腾讯人工智能实验室）
Most commonly used distributed machine learning systems are either synchronous or centralized asynchronous. Synchronous algorithms like AllReduce-SGD perform poorly in a heterogeneous environment, while asynchronous algorithms using a parameter server suffer from 1) communication bottleneck at parameter servers when workers are many, and 2) significantly worse convergence when the traffic to parameter server is congested. Can we design an algorithm that is robust in a heterogeneous environment, while being communication efficient and maintaining the best-possible convergence rate? In this pape…
We present ErasureHead, a new approach for distributed gradient descent (GD) that mitigates system delays by employing approximate gradient coding. Gradient coded distributed GD uses redundancy to exactly recover the gradient at each iteration from a subset of compute nodes. ErasureHead instead uses approximate gradient codes to recover an inexact gradient at each iteration, but with higher delay tolerance. Unlike prior work on gradient coding, we provide a performance analysis that combines both delay and convergence guarantees. We establish that down to a small noise floor, ErasureHead conve…
In this work, we consider the resilience of distributed algorithms based on stochastic gradient descent (SGD) in distributed learning with potentially Byzantine attackers, who could send arbitrary information to the parameter server to disrupt the training process. Toward this end, we propose a new Lipschitz-inspired coordinate-wise median approach (LICM-SGD) to mitigate Byzantine attacks. We show that our LICM-SGD algorithm can resist up to half of the workers being Byzantine attackers, while still converging almost surely to a stationary region in non-convex settings. Also, our LICM-SGD meth…
University of Southern California（南加利福尼亚大学）；University of Illinois at Urbana-Champaign（伊利诺伊大学厄巴纳-香槟分校）
Distributed training of deep nets is an important technique to address some of the present day computing challenges like memory consumption and computational demands. Classical distributed approaches, synchronous or asynchronous, are based on the parameter server architecture, i.e., worker nodes compute gradients which are communicated to the parameter server while updated parameters are returned. Recently, distributed training with AllReduce operations gained popularity as well. While many of those operations seem appealing, little is reported about wall-clock training time improvements. In t…
Anhui Province Key Laboratory of Big Data Analysis and Application（安徽省大数据分析与应用重点实验室）；School of Computer Science and Technology, University of Science and Technology of China（中国科学技术大学计算机科学与技术学院）；School of Data Science, University of Science and Technology of China（中国科学技术大学数据科学学院）
With the increase in the amount of data and the expansion of model scale, distributed parallel training becomes an important and successful technique to address the optimization challenges. Nevertheless, although distributed stochastic gradient descent (SGD) algorithms can achieve a linear iteration speedup, they are limited significantly in practice by the communication cost, making it difficult to achieve a linear time speedup. In this paper, we propose a computation and communication decoupled stochastic gradient descent (CoCoD-SGD) algorithm to run computation and communication in parallel…
North Carolina State University（北卡罗来纳州立大学）；Wuhan University（武汉大学）
The recent advances in sensor technologies and smart devices enable the collaborative collection of a sheer volume of data from multiple information sources. As a promising tool to efficiently extract useful information from such big data, machine learning has been pushed to the forefront and seen great success in a wide range of relevant areas such as computer vision, health care, and financial market analysis. To accommodate the large volume of data, there is a surge of interest in the design of distributed machine learning, among which stochastic gradient descent (SGD) is one of the mostly …
Imperial College London（帝国理工学院）；University of Maryland（马里兰大学）
Coded computation techniques provide robustness against straggling servers in distributed computing, with the following limitations: First, they increase decoding complexity. Second, they ignore computations carried out by straggling servers; and they are typically designed to recover the full gradient, and thus, cannot provide a balance between the accuracy of the gradient and per-iteration completion time. Here we introduce a hybrid approach, called coded partial gradient computation (CPGC), that benefits from the advantages of both coded and uncoded computation schemes, and reduces both the…
Shenzhen Research Institute of Big Data（深圳大数据研究院）；The Chinese University of Hong Kong, Shenzhen（香港中文大学（深圳））；Boston University（波士顿大学）
This paper is concerned with minimizing the average of $n$ cost functions over a network in which agents may communicate and exchange information with each other. We consider the setting where only noisy gradient information is available. To solve the problem, we study the distributed stochastic gradient descent (DSGD) method and perform a non-asymptotic convergence analysis. For strongly convex and smooth objective functions, DSGD asymptotically achieves the optimal network independent convergence rate compared to centralized stochastic gradient descent (SGD). Our main contribution is to char…
We present an optimizer which uses Bayesian optimization to tune the system parameters of distributed stochastic gradient descent (SGD). Given a specific context, our goal is to quickly find efficient configurations which appropriately balance the load between the available machines to minimize the average SGD iteration time. Our experiments consider setups with over thirty parameters. Traditional Bayesian optimization, which uses a Gaussian process as its model, is not well suited to such high dimensional domains. To reduce convergence time, we exploit the available structure. We design a pro…
We propose graph-dependent implicit regularisation strategies for distributed stochastic subgradient descent (Distributed SGD) for convex problems in multi-agent learning. Under the standard assumptions of convexity, Lipschitz continuity, and smoothness, we establish statistical learning rates that retain, up to logarithmic terms, centralised statistical guarantees through implicit regularisation (step size tuning and early stopping) with appropriate dependence on the graph topology. Our approach avoids the need for explicit regularisation in decentralised learning problems, such as adding con…
Weizmann Institute of Science（魏茨曼科学研究所）；TTI Chicago（芝加哥丰田工业大学）
We provide tight finite-time convergence bounds for gradient descent and stochastic gradient descent on quadratic functions, when the gradients are delayed and reflect iterates from $τ$ rounds ago. First, we show that without stochastic noise, delays strongly affect the attainable optimization error: In fact, the error can be as bad as non-delayed gradient descent ran on only $1/τ$ of the gradients. In sharp contrast, we quantify how stochastic noise makes the effect of delays negligible, improving on previous work which only showed this phenomenon asymptotically or for much smaller delays. Al…
IST Austria（奥地利科学技术研究所）；Czech Technical University in Prague（布拉格捷克理工大学）
Machine learning has made tremendous progress in recent years, with models matching or even surpassing humans on a series of specialized tasks. One key element behind the progress of machine learning in recent years has been the ability to train machine learning models in large-scale distributed shared-memory and message-passing environments. Many of these models are trained employing variants of stochastic gradient descent (SGD) based optimization. In this paper, we introduce a general consistency condition covering communication-reduced and asynchronous distributed SGD implementations. Our f…
Mirror descent (MD) is a powerful first-order optimization technique that subsumes several optimization algorithms including gradient descent (GD). In this work, we develop a semi-definite programming (SDP) framework to analyze the convergence rate of MD in centralized and distributed settings under both strongly convex and non-strongly convex assumptions. We view MD with a dynamical system lens and leverage quadratic constraints (QCs) to provide explicit convergence rates based on Lyapunov stability. For centralized MD under strongly convex assumption, we develop a SDP that certifies exponent…
Technical University of Munich（慕尼黑工业大学）；Indian Institute of Science（印度科学学院）；US Army Research Laboratory（美国陆军研究实验室）；Rutgers University（罗格斯大学）
We consider the setting where a master wants to run a distributed stochastic gradient descent (SGD) algorithm on $n$ workers, each having a subset of the data. Distributed SGD may suffer from the effect of stragglers, i.e., slow or unresponsive workers who cause delays. One solution studied in the literature is to wait at each iteration for the responses of the fastest $k<n$ workers before updating the model, where $k$ is a fixed parameter. The choice of the value of $k$ presents a trade-off between the runtime (i.e., convergence rate) of SGD and the error of the model. Towards optimizing the …
University of Science and Technology of China（中国科学技术大学）；Rensselaer Polytechnic Institute（伦斯勒理工学院）；Sun Yat-Sen University（中山大学）
This paper develops a communication-efficient algorithm to solve the stochastic optimization problem defined over a distributed network, aiming at reducing the burdensome communication in applications such as distributed machine learning.Different from the existing works based on quantization and sparsification, we introduce a communication-censoring technique to reduce the transmissions of variables, which leads to our communication-Censored distributed Stochastic Gradient Descent (CSGD) algorithm. Specifically, in CSGD, the latest mini-batch stochastic gradient at a worker will be transmitte…
Imperial College London（伦敦帝国学院）；University of Maryland, College Park（马里兰大学帕克分校）
Distributed gradient descent (DGD) is an efficient way of implementing gradient descent (GD), especially for large data sets, by dividing the computation tasks into smaller subtasks and assigning to different computing servers (CSs) to be executed in parallel. In standard parallel execution, per-iteration waiting time is limited by the execution time of the straggling servers. Coded DGD techniques have been introduced recently, which can tolerate straggling servers via assigning redundant computation tasks to the CSs. In most of the existing DGD schemes, either with coded computation or coded …
This paper introduces Distributed Stein Variational Gradient Descent (DSVGD), a non-parametric generalized Bayesian inference framework for federated learning. DSVGD maintains a number of non-random and interacting particles at a central server to represent the current iterate of the model global posterior. The particles are iteratively downloaded and updated by one of the agents with the end goal of minimizing the global free energy. By varying the number of particles, DSVGD enables a flexible trade-off between per-iteration communication load and number of communication rounds. DSVGD is show…
Modern supervised learning techniques, particularly those using deep nets, involve fitting high dimensional labelled data sets with functions containing very large numbers of parameters. Much of this work is empirical. Interesting phenomena have been observed that require theoretical explanations; however the non-convexity of the loss functions complicates the analysis. Recently it has been proposed that the success of these techniques rests partly in the effectiveness of the simple stochastic gradient descent algorithm in the so called interpolation limit in which all labels are fit perfectly…
We propose a distributed Quantum State Tomography (QST) protocol, named Local Stochastic Factored Gradient Descent (Local SFGD), to learn the low-rank factor of a density matrix over a set of local machines. QST is the canonical procedure to characterize the state of a quantum system, which we formulate as a stochastic nonconvex smooth optimization problem. Physically, the estimation of a low-rank density matrix helps characterizing the amount of noise introduced by quantum computation. Theoretically, we prove the local convergence of Local SFGD for a general class of restricted strongly conve…
We address the issue of speeding up the training of convolutional neural networks by studying a distributed method adapted to stochastic gradient descent. Our parallel optimization setup uses several threads, each applying individual gradient descents on a local variable. We propose a new way of sharing information between different threads based on gossip algorithms that show good consensus convergence properties. Our method called GoSGD has the advantage to be fully asynchronous and decentralized.
