King Abdullah University of Science and Technology（阿卜杜拉国王科技大学）；Skolkovo Institute of Science and Technology（斯科尔科沃科学技术研究院）；Moscow Institute of Physics and Technology（莫斯科物理技术学院）；Mohamed bin Zayed University of Artificial Intelligence（穆罕默德·本·扎耶德人工智能大学）；Institute of Science and Technology Austria（奥地利科学技术研究院）
Aleksandr Beznosikov, Samuel Horváth, Peter Richtárik, Mher Safaryan
备注：
50 pages, 9 figures, 5 tables, 22 theorems and lemmas, 7 new compression operators, 1 algorithm
发表信息：
Journal of Machine Learning Research 2023: https://www.jmlr.org/papers/v24/21-1548.html
In the last few years, various communication compression techniques have emerged as an indispensable tool helping to alleviate the communication bottleneck in distributed learning. However, despite the fact biased compressors often show superior performance in practice when compared to the much more studied and understood unbiased compressors, very little is known about them. In this work we study three classes of biased compression operators, two of which are new, and their performance when applied to (stochastic) gradient descent and distributed (stochastic) gradient descent. We show for the first time that biased compressors can lead to linear convergence rates both in the single node and distributed settings. We prove that distributed compressed SGD method, employed with error feedback mechanism, enjoys the ergodic rate $O\left( δL \exp \left[-\frac{μK}{δL}\right] + \frac{(C + δD)}{Kμ}\right)$, where $δ\ge 1$ is a compression parameter which grows when more compression is applied, $L$ and $μ$ are the smoothness and strong convexity constants, $C$ captures stochastic gradient noise ($C=0$ if full gradients are computed on each node) and $D$ captures the variance of the gradients at the optimum ($D=0$ for over-parameterized models). Further, via a theoretical study of several synthetic and empirical distributions of communicated gradients, we shed light on why and by how much biased compressors outperform their unbiased variants. Finally, we propose several new biased compressors with promising theoretical guarantees and practical performance.
KAUST（阿卜杜拉国王科技大学）；King Abdullah University of Science and Technology (KAUST)（阿卜杜拉国王科技大学（KAUST））
In distributed or federated optimization and learning, communication between the different computing units is often the bottleneck and gradient compression is widely used to reduce the number of bits sent within each communication round of iterative methods. There are two classes of compression operators and separate algorithms making use of them. In the case of unbiased random compressors with bounded variance (e.g., rand-k), the DIANA algorithm of Mishchenko et al. (2019), which implements a variance reduction technique for handling the variance introduced by compression, is the current stat…
We analyze the complexity of biased stochastic gradient methods (SGD), where individual updates are corrupted by deterministic, i.e. biased error terms. We derive convergence results for smooth (non-convex) functions and give improved rates under the Polyak-Lojasiewicz condition. We quantify how the magnitude of the bias impacts the attainable accuracy and the convergence rates (sometimes leading to divergence). Our framework covers many applications where either only biased gradient updates are available, or preferred, over unbiased ones for performance reasons. For instance, in the domain of…
In federated learning (FL) systems, e.g., wireless networks, the communication cost between the clients and the central server can often be a bottleneck. To reduce the communication cost, the paradigm of communication compression has become a popular strategy in the literature. In this paper, we focus on biased gradient compression techniques in non-convex FL problems. In the classical setting of distributed learning, the method of error feedback (EF) is a common technique to remedy the downsides of biased gradient compression. In this work, we study a compressed FL scheme equipped with error …
Sign-based algorithms (e.g. signSGD) have been proposed as a biased gradient compression technique to alleviate the communication bottleneck in training large neural networks across multiple workers. We show simple convex counter-examples where signSGD does not converge to the optimum. Further, even when it does converge, signSGD may generalize poorly when compared with SGD. These issues arise because of the biased nature of the sign compression operator. We then show that using error-feedback, i.e. incorporating the error made by the compression operator into the next step, overcomes these is…
We study gradient compression methods to alleviate the communication bottleneck in data-parallel distributed optimization. Despite the significant attention received, current compression schemes either do not scale well or fail to achieve the target test accuracy. We propose a new low-rank gradient compressor based on power iteration that can i) compress gradients rapidly, ii) efficiently aggregate the compressed gradients using all-reduce, and iii) achieve test performance on par with SGD. The proposed algorithm is the only method evaluated that achieves consistent wall-clock speedups when be…
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.
Large-scale distributed training requires significant communication bandwidth for gradient exchange that limits the scalability of multi-node training, and requires expensive high-bandwidth network infrastructure. The situation gets even worse with distributed training on mobile devices (federated learning), which suffers from higher latency, lower throughput, and intermittent poor connections. In this paper, we find 99.9% of the gradient exchange in distributed SGD is redundant, and propose Deep Gradient Compression (DGC) to greatly reduce the communication bandwidth. To preserve accuracy dur…
Recent advances in distributed optimization and learning have shown that communication compression is one of the most effective means of reducing communication. While there have been many results on convergence rates under communication compression, a theoretical lower bound is still missing. Analyses of algorithms with communication compression have attributed convergence to two abstract properties: the unbiased property or the contractive property. They can be applied with either unidirectional compression (only messages from workers to server are compressed) or bidirectional compression. In…
Mask-Encoded Sparsification: Mitigating Biased Gradients in Communication-Efficient Split Learning
Key Laboratory of Water Big Data Technology of Ministry of Water Resources, Hohai University, Nanjing, China（水利部水大数据技术重点实验室，河海大学，南京，中国）；National Key Laboratory for Novel Software Technology, Nanjing University, Nanjing, China（新型软件技术国家实验室，南京大学，南京，中国）；Nanjing University of Aeronautics（南京航空航天大学）
The University of Hong Kong（香港大学）；University of Illinois Urbana-Champaign（伊利诺伊大学厄巴纳-香槟分校）；Amazon Web Services（亚马逊云科技）；ByteDance Inc.（字节跳动有限公司）
Communication overhead severely hinders the scalability of distributed machine learning systems. Recently, there has been a growing interest in using gradient compression to reduce the communication overhead of the distributed training. However, there is little understanding of applying gradient compression to adaptive gradient methods. Moreover, its performance benefits are often limited by the non-negligible compression overhead. In this paper, we first introduce a novel adaptive gradient method with gradient compression. We show that the proposed method has a convergence rate of $\mathcal{O…
Mohamed bin Zayed University of Artificial Intelligence（穆罕默德·本·扎耶德人工智能大学）；King Abdullah University of Science and Technology（阿卜杜拉国王科技大学）；Dell Technologies（戴尔科技集团）；Comenius University（夸美纽斯大学）
Modern deep learning models are often trained in parallel over a collection of distributed machines to reduce training time. In such settings, communication of model updates among machines becomes a significant performance bottleneck and various lossy update compression techniques have been proposed to alleviate this problem. In this work, we introduce a new, simple yet theoretically and practically effective compression technique: natural compression (NC). Our technique is applied individually to all entries of the to-be-compressed update vector and works by randomized rounding to the nearest…
Moscow Institute of Physics and Technology（莫斯科物理技术学院）
In this thesis, we propose new theoretical frameworks for the analysis of stochastic and distributed methods with error compensation and local updates. Using these frameworks, we develop more than 20 new optimization methods, including the first linearly converging Error-Compensated SGD and the first linearly converging Local-SGD for arbitrarily heterogeneous local functions. Moreover, the thesis contains several new distributed methods with unbiased compression for distributed non-convex optimization problems. The derived complexity results for these methods outperform the previous best-known…
We study COMP-AMS, a distributed optimization framework based on gradient averaging and adaptive AMSGrad algorithm. Gradient compression with error feedback is applied to reduce the communication cost in the gradient transmission process. Our convergence analysis of COMP-AMS shows that such compressed gradient averaging strategy yields same convergence rate as standard AMSGrad, and also exhibits the linear speedup effect w.r.t. the number of local workers. Compared with recently proposed protocols on distributed adaptive methods, COMP-AMS is simple and convenient. Numerical experiments are con…
Large-scale machine learning models are often trained by parallel stochastic gradient descent algorithms. However, the communication cost of gradient aggregation and model synchronization between the master and worker nodes becomes the major obstacle for efficient learning as the number of workers and the dimension of the model increase. In this paper, we propose DORE, a DOuble REsidual compression stochastic gradient descent algorithm, to reduce over $95\%$ of the overall communication such that the obstacle can be immensely mitigated. Our theoretical analyses demonstrate that the proposed st…
Compressed communication, in the form of sparsification or quantization of stochastic gradients, is employed to reduce communication costs in distributed data-parallel training of deep neural networks. However, there exists a discrepancy between theory and practice: while theoretical analysis of most existing compression methods assumes compression is applied to the gradients of the entire model, many practical implementations operate individually on the gradients of each layer of the model. In this paper, we prove that layer-wise compression is, in theory, better, because the convergence rate…
Due to the high communication cost in distributed and federated learning, methods relying on compressed communication are becoming increasingly popular. Besides, the best theoretically and practically performing gradient-type methods invariably rely on some form of acceleration/momentum to reduce the number of communications (faster convergence), e.g., Nesterov's accelerated gradient descent (Nesterov, 1983, 2004) and Adam (Kingma and Ba, 2014). In order to combine the benefits of communication compression and convergence acceleration, we propose a \emph{compressed and accelerated} gradient me…
CompressedScaffnew: The First Theoretical Double Acceleration of Communication from Local Training and Compression in Distributed Optimization
King Abdullah University of Science and Technology (KAUST)（阿卜杜拉国王科技大学）；SDAIA-KAUST Center of Excellence in Data Science and Artificial Intelligence (SDAIA-KAUST AI)（SDAIA-KAUST数据科学与人工智能卓越中心）；Brno University of Technology（布尔诺理工大学）；Kempelen Institute of Intelligent Technologies (KInIT)（肯佩伦智能技术研究所）
Lossy gradient compression, with either unbiased or biased compressors, has become a key tool to avoid the communication bottleneck in centrally coordinated distributed training of machine learning models. We analyze the performance of two standard and general types of methods: (i) distributed quantized SGD (D-QSGD) with arbitrary unbiased quantizers and (ii) distributed SGD with error-feedback and biased compressors (D-EF-SGD) in the heterogeneous (non-iid) data setting. Our results indicate that D-EF-SGD is much less affected than D-QSGD by non-iid data, but both methods can suffer a slowdow…
Information compression is essential to reduce communication cost in distributed optimization over peer-to-peer networks. This paper proposes a communication-efficient linearly convergent distributed (COLD) algorithm to solve strongly convex optimization problems. By compressing innovation vectors, which are the differences between decision vectors and their estimates, COLD is able to achieve linear convergence for a class of $δ$-contracted compressors. We explicitly quantify how the compression affects the convergence rate and show that COLD matches the same rate of its uncompressed version. …
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…
Institute of Control Sciences of RAS（俄罗斯科学院控制科学研究所）；Moscow Institute of Physics and Technology（莫斯科物理技术学院）
Distributed optimization methods are often applied to solving huge-scale problems like training neural networks with millions and even billions of parameters. In such applications, communicating full vectors, e.g., (stochastic) gradients, iterates, is prohibitively expensive, especially when the number of workers is large. Communication compression is a powerful approach to alleviating this issue, and, in particular, methods with biased compression and error compensation are extremely popular due to their practical efficiency. Sahu et al. (2021) propose a new analysis of Error Compensated SGD …
Highly distributed training of Deep Neural Networks (DNNs) on future compute platforms (offering 100 of TeraOps/s of computational capacity) is expected to be severely communication constrained. To overcome this limitation, new gradient compression techniques are needed that are computationally friendly, applicable to a wide variety of layers seen in Deep Neural Networks and adaptable to variations in network architectures as well as their hyper-parameters. In this paper we introduce a novel technique - the Adaptive Residual Gradient Compression (AdaComp) scheme. AdaComp is based on localized …
Greedy Low-Rank Gradient Compression for Distributed Learning with Convergence Guarantees
School of Mathematical Sciences, Peking University（北京大学数学科学学院）；Center for Data Science, Peking University（北京大学数据科学中心）；School of Software, Beihang University（北航软件学院）；School of Life Sciences, Peking University（北京大学生命科学学院）；Center for Machine Learning Research, Peking University（北京大学机器学习研究中心）
École Polytechnique（巴黎综合理工学院）；Institut Polytechnique de Paris（巴黎理工学院）
We develop a new approach to tackle communication constraints in a distributed learning problem with a central server. We propose and analyze a new algorithm that performs bidirectional compression and achieves the same convergence rate as algorithms using only uplink (from the local workers to the central server) compression. To obtain this improvement, we design MCM, an algorithm such that the downlink compression only impacts local models, while the global model is preserved. As a result, and contrary to previous works, the gradients on local servers are computed on perturbed models. Conseq…
Institut Polytechnique de Paris（巴黎理工学院）；JD Explore Academy（京东探索研究院）；King Abdullah University of Science and Technology（阿卜杜拉国王科技大学）
Despite their high computation and communication costs, Newton-type methods remain an appealing option for distributed training due to their robustness against ill-conditioned convex problems. In this work, we study ommunication compression and aggregation mechanisms for curvature information in order to reduce these costs while preserving theoretically superior local convergence guarantees. We prove that the recently developed class of three point compressors (3PC) of Richtarik et al. [2022] for gradient communication can be generalized to Hessian communication as well. This result opens up a…
Moscow Institute of Physics and Technology（莫斯科物理技术学院）；Yandex；King Abdullah University of Science and Technology（阿卜杜拉国王科技大学）
We develop and analyze MARINA: a new communication efficient method for non-convex distributed learning over heterogeneous datasets. MARINA employs a novel communication compression strategy based on the compression of gradient differences that is reminiscent of but different from the strategy employed in the DIANA method of Mishchenko et al. (2019). Unlike virtually all competing distributed first-order methods, including DIANA, ours is based on a carefully designed biased gradient estimator, which is the key to its superior theoretical and practical performance. The communication complexity …
College of Computer Science, Zhejiang University（浙江大学计算机科学与技术学院）；School of Software Technology, Zhejiang University（浙江大学软件学院）
With the rapid increase of big data, distributed Machine Learning (ML) has been widely applied in training large-scale models. Stochastic Gradient Descent (SGD) is arguably the workhorse algorithm of ML. Distributed ML models trained by SGD involve large amounts of gradient communication, which limits the scalability of distributed ML. Thus, it is important to compress the gradients for reducing communication. In this paper, we propose FastSGD, a Fast compressed SGD framework for distributed ML. To achieve a high compression ratio at a low cost, FastSGD represents the gradients as key-value pa…
KAUST（阿卜杜拉国王科技大学）；Institut Polytechnique de Paris（巴黎理工学院）；MIPT（莫斯科物理技术学院）
We propose Adaptive Compressed Gradient Descent (AdaCGD) - a novel optimization algorithm for communication-efficient training of supervised machine learning models with adaptive compression level. Our approach is inspired by the recently proposed three point compressor (3PC) framework of Richtarik et al. (2022), which includes error feedback (EF21), lazily aggregated gradient (LAG), and their combination as special cases, and offers the current state-of-the-art rates for these methods under weak assumptions. While the above mechanisms offer a fixed compression level, or adapt between two extr…
LASER: Linear Compression in Wireless Distributed Optimization
School of Computer and Communication Sciences, EPFL（洛桑联邦理工学院计算机与通信科学学院）；Department of Electrical and Computer Engineering, UT Austin（德克萨斯大学奥斯汀分校电气与计算机工程系）
To address the high communication costs of distributed machine learning, a large body of work has been devoted in recent years to designing various compression strategies, such as sparsification and quantization, and optimization algorithms capable of using them. Recently, Safaryan et al. (2021) pioneered a dramatically different compression design approach: they first use the local training data to form local smoothness matrices and then propose to design a compressor capable of exploiting the smoothness information contained therein. While this novel approach leads to substantial savings in …
Distributed data mining is an emerging research topic to effectively and efficiently address hard data mining tasks using big data, which are partitioned and computed on different worker nodes, instead of one centralized server. Nevertheless, distributed learning methods often suffer from the communication bottleneck when the network bandwidth is limited or the size of model is large. To solve this critical issue, many gradient compression methods have been proposed recently to reduce the communication cost for multiple optimization algorithms. However, the current applications of gradient com…
Evaluation and Optimization of Gradient Compression for Distributed Deep Learning
The Hong Kong University of Science and Technology（香港科技大学）；Hong Kong Baptist University（香港浸会大学）；Harbin Institute of Technology, Shenzhen（哈尔滨工业大学（深圳））；The Hong Kong University of Science and Technology (Guangzhou)（香港科技大学（广州））
Massive amounts of data have led to the training of large-scale machine learning models on a single worker inefficient. Distributed machine learning methods such as Parallel-SGD have received significant interest as a solution to tackle this problem. However, the performance of distributed systems does not scale linearly with the number of workers due to the high network communication cost for synchronizing gradients and parameters. Researchers have proposed techniques such as quantization and sparsification to alleviate this problem by compressing the gradients. Most of the compression scheme…
Distributed Online Convex Optimization with Compressed Communication: Optimal Regret and Applications
National Key Laboratory for Novel Software Technology, Nanjing University（南京大学计算机软件新技术国家重点实验室）；School of Artificial Intelligence, Nanjing University（南京大学人工智能学院）
Cornell University（康奈尔大学）；Stanford University（斯坦福大学）；Indian Institute of Science（印度科学学院）
We study goodness-of-fit of discrete distributions in the distributed setting, where samples are divided between multiple users who can only release a limited amount of information about their samples due to various information constraints. Recently, a subset of the authors showed that having access to a common random seed (i.e., shared randomness) leads to a significant reduction in the sample complexity of this problem. In this work, we provide a complete understanding of the interplay between the amount of shared randomness available, the stringency of information constraints, and the sampl…
Large-scale distributed training is increasingly becoming communication bound. Many gradient compression algorithms have been proposed to reduce the communication overhead and improve scalability. However, it has been observed that in some cases gradient compression may even harm the performance of distributed training. In this paper, we propose MergeComp, a compression scheduler to optimize the scalability of communication-efficient distributed training. It automatically schedules the compression operations to optimize the performance of compression algorithms without the knowledge of model a…
Moscow Institute of Physics and Technology（莫斯科物理技术学院）；HSE University（高等经济大学）；IITP RAS（俄罗斯科学院信息传输问题研究所）；Adyghe State University（阿迪格国立大学）
Variational inequalities are an important tool, which includes minimization, saddles, games, fixed-point problems. Modern large-scale and computationally expensive practical applications make distributed methods for solving these problems popular. Meanwhile, most distributed systems have a basic problem - a communication bottleneck. There are various techniques to deal with it. In particular, in this paper we consider a combination of two popular approaches: compression and data similarity. We show that this synergy can be more effective than each of the approaches separately in solving distri…
The performance and efficiency of distributed machine learning (ML) depends significantly on how long it takes for nodes to exchange state changes. Overly-aggressive attempts to reduce communication often sacrifice final model accuracy and necessitate additional ML techniques to compensate for this loss, limiting their generality. Some attempts to reduce communication incur high computation overhead, which makes their performance benefits visible only over slow networks. We present 3LC, a lossy compression scheme for state change traffic that strikes balance between multiple goals: traffic red…
King Abdullah University of Science and Technology (KAUST)（阿卜杜拉国王科技大学）
The recent many-fold increase in the size of deep neural networks makes efficient distributed training challenging. Many proposals exploit the compressibility of the gradients and propose lossy compression techniques to speed up the communication stage of distributed training. Nevertheless, compression comes at the cost of reduced model quality and extra computation overhead. In this work, we design an efficient compressor with minimal overhead. Noting the sparsity of the gradients, we propose to model the gradients as random variables distributed according to some sparsity-inducing distributi…
Moscow Institute of Physics and Technology（莫斯科物理技术学院）；King Abdullah University of Science and Technology（阿卜杜拉国王科技大学）
In order to mitigate the high communication cost in distributed and federated learning, various vector compression schemes, such as quantization, sparsification and dithering, have become very popular. In designing a compression method, one aims to communicate as few bits as possible, which minimizes the cost per communication round, while at the same time attempting to impart as little distortion (variance) to the communicated messages as possible, which minimizes the adverse effect of the compression on the overall number of communication rounds. However, intuitively, these two goals are fun…
Gradient compression (GC) is a promising approach to addressing the communication bottleneck in distributed deep learning (DDL). However, it is challenging to find the optimal compression strategy for applying GC to DDL because of the intricate interactions among tensors. To fully unleash the benefits of GC, two questions must be addressed: 1) How to express all compression strategies and the corresponding interactions among tensors of any DDL training job? 2) How to quickly select a near-optimal compression strategy? In this paper, we propose ByteComp to answer these questions. It first desig…
King Abdullah University of Science and Technology (KAUST)（阿卜杜拉国王科技大学）
Communicating information, like gradient vectors, between computing nodes in distributed and federated learning is typically an unavoidable burden, resulting in scalability issues. Indeed, communication might be slow and costly. Recent advances in communication-efficient training algorithms have reduced this bottleneck by using compression techniques, in the form of sparsification, quantization, or low-rank approximation. Since compression is a lossy, or inexact, process, the iteration complexity is typically worsened; but the total communication complexity can improve significantly, possibly …
University of Pennsylvania（宾夕法尼亚大学）；University of California, Berkeley（加州大学伯克利分校）
Recently, researchers proposed various low-precision gradient compression, for efficient communication in large-scale distributed optimization. Based on these work, we try to reduce the communication complexity from a new direction. We pursue an ideal bijective mapping between two spaces of gradient distribution, so that the mapped gradient carries greater information entropy after the compression. In our setting, all servers should share a reference gradient in advance, and they communicate via the normalized gradients, which are the subtraction or quotient, between current gradients and the …
Fraunhofer Heinrich Hertz Institute（弗劳恩霍夫海因里希·赫兹研究所）；Technische Universität Berlin（柏林工业大学）；Max Planck Institute for Informatics（马克斯·普朗克信息学研究所）；Korea University（高丽大学）
Currently, progressively larger deep neural networks are trained on ever growing data corpora. As this trend is only going to increase in the future, distributed training schemes are becoming increasingly relevant. A major issue in distributed training is the limited communication bandwidth between contributing nodes or prohibitive communication cost in general. These challenges become even more pressing, as the number of computation nodes increases. To counteract this development we propose sparse binary compression (SBC), a compression framework that allows for a drastic reduction of communi…
Distributed training of deep neural networks has received significant research interest, and its major approaches include implementations on multiple GPUs and clusters. Parallelization can dramatically improve the efficiency of training deep and complicated models with large-scale data. A fundamental barrier against the speedup of DNN training, however, is the trade-off between computation and communication time. In other words, increasing the number of worker nodes decreases the time consumed in computation while simultaneously increasing communication overhead under constrained network bandw…
