Shadowheart SGD: Distributed Asynchronous SGD with Optimal Time Complexity Under Arbitrary Computation and Communication Heterogeneity
King Abdullah University of Science and Technology（阿卜杜拉国王科技大学）；AIRI；Skolkovo Institute of Science and Technology（斯科尔科沃科学技术研究院）；University of Pavia（帕维亚大学）
Alexander Tyurin, Marta Pozzi, Ivan Ilin, Peter Richtárik
We consider nonconvex stochastic optimization problems in the asynchronous centralized distributed setup where the communication times from workers to a server can not be ignored, and the computation and communication times are potentially different for all workers. Using an unbiassed compression technique, we develop a new method-Shadowheart SGD-that provably improves the time complexities of all previous centralized methods. Moreover, we show that the time complexity of Shadowheart SGD is optimal in the family of centralized methods with compressed communication. We also consider the bidirectional setup, where broadcasting from the server to the workers is non-negligible, and develop a corresponding method.
Okinawa Institute of Science and Technology（冲绳科学技术大学院大学）；National University of Singapore（新加坡国立大学）；Toyota Motor Corporation（丰田汽车公司）；University of Zurich（苏黎世大学）
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…
Large scale machine learning is increasingly relying on distributed optimization, whereby several machines contribute to the training process of a statistical model. In this work we study the performance of asynchronous, distributed settings, when applying sparsification, a technique used to reduce communication overheads. In particular, for the first time in an asynchronous, non-convex setting, we theoretically prove that, in presence of staleness, sparsification does not harm SGD performance: the ergodic convergence rate matches the known result of standard SGD, that is $\mathcal{O} \left( 1…
Stochastic gradient descent~(SGD) and its variants have become more and more popular in machine learning due to their efficiency and effectiveness. To handle large-scale problems, researchers have recently proposed several parallel SGD methods for multicore systems. However, existing parallel SGD methods cannot achieve satisfactory performance in real applications. In this paper, we propose a fast asynchronous parallel SGD method, called AsySVRG, by designing an asynchronous strategy to parallelize the recently proposed SGD variant called stochastic variance reduced gradient~(SVRG). Both theor…
We study the asynchronous stochastic gradient descent algorithm for distributed training over $n$ workers which have varying computation and communication frequency over time. In this algorithm, workers compute stochastic gradients in parallel at their own pace and return those to the server without any synchronization. Existing convergence rates of this algorithm for non-convex smooth objectives depend on the maximum gradient delay $τ_{\max}$ and show that an $ε$-stationary point is reached after $\mathcal{O}\!\left(σ^2ε^{-2}+ τ_{\max}ε^{-1}\right)$ iterations, where $σ$ denotes the variance …
Communication cost is the main bottleneck for the design of effective distributed learning algorithms. Recently, event-triggered techniques have been proposed to reduce the exchanged information among compute nodes and thus alleviate the communication cost. However, most existing event-triggered approaches only consider heuristic event-triggered thresholds. They also ignore the impact of computation and network delay, which play an important role on the training performance. In this paper, we propose an Asynchronous Event-triggered Stochastic Gradient Descent (SGD) framework, called AET-SGD, t…
We provide the first theoretical analysis on the convergence rate of the asynchronous stochastic variance reduced gradient (SVRG) descent algorithm on non-convex optimization. Recent studies have shown that the asynchronous stochastic gradient descent (SGD) based algorithms with variance reduction converge with a linear convergent rate on convex problems. However, there is no work to analyze asynchronous SGD with variance reduction technique on non-convex problem. In this paper, we study two asynchronous parallel implementations of SVRG: one is on a distributed memory system and the other is o…
University of Illinois, Urbana-Champaign（伊利诺伊大学厄巴纳-香槟分校）
We propose Zeno++, a new robust asynchronous Stochastic Gradient Descent~(SGD) procedure which tolerates Byzantine failures of the workers. In contrast to previous work, Zeno++ removes some unrealistic restrictions on worker-server communications, allowing for fully asynchronous updates from anonymous workers, arbitrarily stale worker updates, and the possibility of an unbounded number of Byzantine workers. The key idea is to estimate the descent of the loss value after the candidate gradient is applied, where large descent values indicate that the update results in optimization progress. We p…
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…
Understanding the convergence performance of asynchronous stochastic gradient descent method (Async-SGD) has received increasing attention in recent years due to their foundational role in machine learning. To date, however, most of the existing works are restricted to either bounded gradient delays or convex settings. In this paper, we focus on Async-SGD and its variant Async-SGDI (which uses increasing batch size) for non-convex optimization problems with unbounded gradient delays. We prove $o(1/\sqrt{k})$ convergence rate for Async-SGD and $o(1/k)$ for Async-SGDI. Also, a unifying sufficien…
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…
Stanford University（斯坦福大学）；University of Wisconsin-Madison（威斯康星大学麦迪逊分校）
Stochastic gradient descent (SGD) is a ubiquitous algorithm for a variety of machine learning problems. Researchers and industry have developed several techniques to optimize SGD's runtime performance, including asynchronous execution and reduced precision. Our main result is a martingale-based analysis that enables us to capture the rich noise models that may arise from such techniques. Specifically, we use our new analysis in three ways: (1) we derive convergence rates for the convex case (Hogwild!) with relaxed assumptions on the sparsity of the problem; (2) we analyze asynchronous SGD algo…
As deep learning models are usually massive and complex, distributed learning is essential for increasing training efficiency. Moreover, in many real-world application scenarios like healthcare, distributed learning can also keep the data local and protect privacy. A popular distributed learning strategy is federated learning, where there is a central server storing the global model and a set of local computing nodes updating the model parameters with their corresponding data. The updated model parameters will be processed and transmitted to the central server, which leads to heavy communicati…
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…
Modern machine learning frameworks can train neural networks using multiple nodes in parallel, each computing parameter updates with stochastic gradient descent (SGD) and sharing them asynchronously through a central parameter server. Due to communication overhead and bottlenecks, the total throughput of SGD updates in a cluster scales sublinearly, saturating as the number of nodes increases. In this paper, we present a solution to predicting training throughput from profiling traces collected from a single-node configuration. Our approach is able to model the interaction of multiple nodes and…
Asynchronous distributed stochastic gradient descent methods have trouble converging because of stale gradients. A gradient update sent to a parameter server by a client is stale if the parameters used to calculate that gradient have since been updated on the server. Approaches have been proposed to circumvent this problem that quantify staleness in terms of the number of elapsed updates. In this work, we propose a novel method that quantifies staleness in terms of moving averages of gradient statistics. We show that this method outperforms previous methods with respect to convergence speed an…
Distributed Stochastic Gradient Descent (SGD) when run in a synchronous manner, suffers from delays in waiting for the slowest learners (stragglers). Asynchronous methods can alleviate stragglers, but cause gradient staleness that can adversely affect convergence. In this work we present a novel theoretical characterization of the speed-up offered by asynchronous methods by analyzing the trade-off between the error in the trained model and the actual training runtime (wallclock time). The novelty in our work is that our runtime analysis considers random straggler delays, which helps us design …
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…
Asynchronous distributed machine learning solutions have proven very effective so far, but always assuming perfectly functioning workers. In practice, some of the workers can however exhibit Byzantine behavior, caused by hardware failures, software bugs, corrupt data, or even malicious attacks. We introduce \emph{Kardam}, the first distributed asynchronous stochastic gradient descent (SGD) algorithm that copes with Byzantine workers. Kardam consists of two complementary components: a filtering and a dampening component. The first is scalar-based and ensures resilience against $\frac{1}{3}$ Byz…
Yale University（耶鲁大学）；University of Central Florida（中佛罗里达大学）；University of Illinois at Urbana-Champaign（伊利诺伊大学厄巴纳-香槟分校）
We propose ACProp (Asynchronous-centering-Prop), an adaptive optimizer which combines centering of second momentum and asynchronous update (e.g. for $t$-th update, denominator uses information up to step $t-1$, while numerator uses gradient at $t$-th step). ACProp has both strong theoretical properties and empirical performance. With the example by Reddi et al. (2018), we show that asynchronous optimizers (e.g. AdaShift, ACProp) have weaker convergence condition than synchronous optimizers (e.g. Adam, RMSProp, AdaBelief); within asynchronous optimizers, we show that centering of second momentu…
Institute of Science and Technology Austria (ISTA)（奥地利科学技术研究所（ISTA））；University of Surrey（萨里大学）；ETH Zurich（苏黎世联邦理工学院）
Decentralized optimization is emerging as a viable alternative for scalable distributed machine learning, but also introduces new challenges in terms of synchronization costs. To this end, several communication-reduction techniques, such as non-blocking communication, quantization, and local steps, have been explored in the decentralized setting. Due to the complexity of analyzing optimization in such a relaxed setting, this line of work often assumes \emph{global} communication rounds, which require additional synchronization. In this paper, we consider decentralized optimization in the simpl…
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…
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…
University of Science and Technology of China（中国科学技术大学）；Peking University（北京大学）；Microsoft Research（微软研究院）；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）
With the fast development of deep learning, it has become common to learn big neural networks using massive training data. Asynchronous Stochastic Gradient Descent (ASGD) is widely adopted to fulfill this task for its efficiency, which is, however, known to suffer from the problem of delayed gradients. That is, when a local worker adds its gradient to the global model, the global model may have been updated by other workers and this gradient becomes "delayed". We propose a novel technology to compensate this delay, so as to make the optimization behavior of ASGD closer to that of sequential SG…
The performance of fully synchronized distributed systems has faced a bottleneck due to the big data trend, under which asynchronous distributed systems are becoming a major popularity due to their powerful scalability. In this paper, we study the generalization performance of stochastic gradient descent (SGD) on a distributed asynchronous system. The system consists of multiple worker machines that compute stochastic gradients which are further sent to and aggregated on a common parameter server to update the variables, and the communication in the system suffers from possible delays. Under t…
University of Illinois at Urbana-Champaign（伊利诺伊大学厄巴纳-香槟分校）；Adobe Research（奥多比研究院）
The ability to train large-scale neural networks has resulted in state-of-the-art performance in many areas of computer vision. These results have largely come from computational break throughs of two forms: model parallelism, e.g. GPU accelerated training, which has seen quick adoption in computer vision circles, and data parallelism, e.g. A-SGD, whose large scale has been used mostly in industry. We report early experiments with a system that makes use of both model parallelism and data parallelism, we call GPU A-SGD. We show using GPU A-SGD it is possible to speed up training of large convo…
IBM T. J. Watson Research Center（IBM托马斯·J·沃森研究中心）；University of Rochester（罗切斯特大学）
Deep neural networks have been shown to achieve state-of-the-art performance in several machine learning tasks. Stochastic Gradient Descent (SGD) is the preferred optimization algorithm for training these networks and asynchronous SGD (ASGD) has been widely adopted for accelerating the training of large-scale deep networks in a distributed computing environment. However, in practice it is quite challenging to tune the training hyperparameters (such as learning rate) when using ASGD so as achieve convergence and linear speedup, since the stability of the optimization algorithm is strongly influ…
Distributed learning has become a hot research topic due to its wide application in clusterbased large-scale learning, federated learning, edge computing and so on. Most traditional distributed learning methods typically assume no failure or attack. However, many unexpected cases, such as communication failure and even malicious attack, may happen in real applications. Hence, Byzantine learning (BL), which refers to distributed learning with failure or attack, has recently attracted much attention. Most existing BL methods are synchronous, which are impractical in some applications due to hete…
In this paper, we present GossipGraD - a gossip communication protocol based Stochastic Gradient Descent (SGD) algorithm for scaling Deep Learning (DL) algorithms on large-scale systems. The salient features of GossipGraD are: 1) reduction in overall communication complexity from Θ(log(p)) for p compute nodes in well-studied SGD to O(1), 2) model diffusion such that compute nodes exchange their updates (gradients) indirectly after every log(p) steps, 3) rotation of communication partners for facilitating direct diffusion of gradients, 4) asynchronous distributed shuffle of samples during the f…
Towards Understanding the Generalizability of Delayed Stochastic Gradient Descent
Intelligent Game and Decision Lab（智能游戏与决策实验室）；College of Computer Science and Technology（计算机科学与技术学院）；National University of Defense Technology（国防科技大学）；Sun Yat-sen University（中山大学）；JD Explore Academy（京东探索研究院）
Stochastic Gradient Descent (SGD) is very useful in optimization problems with high-dimensional non-convex target functions, and hence constitutes an important component of several Machine Learning and Data Analytics methods. Recently there have been significant works on understanding the parallelism inherent to SGD, and its convergence properties. Asynchronous, parallel SGD (AsyncPSGD) has received particular attention, due to observed performance benefits. On the other hand, asynchrony implies inherent challenges in understanding the execution of the algorithm and its convergence, stemming f…
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…
Distributed training algorithms of deep neural networks show impressive convergence speedup properties on very large problems. However, they inherently suffer from communication related slowdowns and communication topology becomes a crucial design choice. Common approaches supported by most machine learning frameworks are: 1) Synchronous decentralized algorithms relying on a peer-to-peer All Reduce topology that is sensitive to stragglers and communication delays. 2) Asynchronous centralised algorithms with a server based topology that is prone to communication bottleneck. Researchers also sug…
Carnegie Mellon University（卡内基梅隆大学）；Massachusetts Institute of Technology（麻省理工学院）
We study optimization algorithms based on variance reduction for stochastic gradient descent (SGD). Remarkable recent progress has been made in this direction through development of algorithms like SAG, SVRG, SAGA. These algorithms have been shown to outperform SGD, both theoretically and empirically. However, asynchronous versions of these algorithms---a crucial requirement for modern large-scale applications---have not been studied. We bridge this gap by presenting a unifying framework for many variance reduction techniques. Subsequently, we propose an asynchronous algorithm grounded in our …
Hong Kong University of Science and Technology（香港科技大学）
With the recent proliferation of large-scale learning problems,there have been a lot of interest on distributed machine learning algorithms, particularly those that are based on stochastic gradient descent (SGD) and its variants. However, existing algorithms either suffer from slow convergence due to the inherent variance of stochastic gradients, or have a fast linear convergence rate but at the expense of poorer solution quality. In this paper, we combine their merits by proposing a fast distributed asynchronous SGD-based algorithm with variance reduction. A constant learning rate can be used…
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…
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…
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…
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…
Stochastic Gradient Descent (SGD) is a fundamental algorithm in machine learning, representing the optimization backbone for training several classic models, from regression to neural networks. Given the recent practical focus on distributed machine learning, significant work has been dedicated to the convergence properties of this algorithm under the inconsistent and noisy updates arising from execution in a distributed environment. However, surprisingly, the convergence properties of this classic algorithm in the standard shared-memory model are still not well-understood. In this work, we ad…
Freya PAGE: First Optimal Time Complexity for Large-Scale Nonconvex Finite-Sum Optimization with Heterogeneous Asynchronous Computations
King Abdullah University of Science and Technology（阿卜杜拉国王科技大学）；AIRI；Skolkovo Institute of Science and Technology（斯科尔科沃科学技术研究院）；KAUST（阿卜杜拉国王科技大学）；Skoltech（斯科尔泰克科技大学）
Courant Institute, NYU（纽约大学柯朗研究所）；Center for Data Science, NYU（纽约大学数据科学中心）；Facebook AI Research（脸书人工智能研究院）
We study the problem of stochastic optimization for deep learning in the parallel computing environment under communication constraints. A new algorithm is proposed in this setting where the communication and coordination of work among concurrent processes (local workers), is based on an elastic force which links the parameters they compute with a center variable stored by the parameter server (master). The algorithm enables the local workers to perform more exploration, i.e. the algorithm allows the local variables to fluctuate further from the center variable by reducing the amount of commun…
