Decentralized stochastic optimization methods have gained a lot of attention recently, mainly because of their cheap per iteration cost, data locality, and their communication-efficiency. In this paper we introduce a unified convergence analysis that covers a large variety of decentralized SGD methods which so far have required different intuitions, have different applications, and which have been developed separately in various communities.
Our algorithmic framework covers local SGD updates and synchronous and pairwise gossip updates on adaptive network topology. We derive universal convergence rates for smooth (convex and non-convex) problems and the rates interpolate between the heterogeneous (non-identically distributed data) and iid-data settings, recovering linear convergence rates in many special cases, for instance for over-parametrized models. Our proofs rely on weak assumptions (typically improving over prior work in several aspects) and recover (and improve) the best known complexity results for a host of important scenarios, such as for instance coorperative SGD and federated averaging (local SGD).
University of California, Los Angeles（加利福尼亚大学洛杉矶分校）；US Army Research Lab（美国陆军研究实验室）
In this paper, we propose and analyze SQuARM-SGD, a communication-efficient algorithm for decentralized training of large-scale machine learning models over a network. In SQuARM-SGD, each node performs a fixed number of local SGD steps using Nesterov's momentum and then sends sparsified and quantized updates to its neighbors regulated by a locally computable triggering criterion. We provide convergence guarantees of our algorithm for general (non-convex) and convex smooth objectives, which, to the best of our knowledge, is the first theoretical analysis for compressed decentralized SGD with mo…
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 California, Los Angeles（加利福尼亚大学洛杉矶分校）；US Army Research Lab（美国陆军研究实验室）
In this paper, we propose and analyze SPARQ-SGD, which is an event-triggered and compressed algorithm for decentralized training of large-scale machine learning models. Each node can locally compute a condition (event) which triggers a communication where quantized and sparsified local model parameters are sent. In SPARQ-SGD each node takes at least a fixed number ($H$) of local gradient steps and then checks if the model parameters have significantly changed compared to its last update; it communicates further compressed model parameters only when there is a significant change, as specified b…
Peking University（北京大学）；Stevens Institute of Technology（史蒂文斯理工学院）
Recently, the technique of local updates is a powerful tool in centralized settings to improve communication efficiency via periodical communication. For decentralized settings, it is still unclear how to efficiently combine local updates and decentralized communication. In this work, we propose an algorithm named as LD-SGD, which incorporates arbitrary update schemes that alternate between multiple Local updates and multiple Decentralized SGDs, and provide an analytical framework for LD-SGD. Under the framework, we present a sufficient condition to guarantee the convergence. We show that LD-S…
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…
Alibaba Group（阿里巴巴集团）；University of Pennsylvania（宾夕法尼亚大学）
The scale of deep learning nowadays calls for efficient distributed training algorithms. Decentralized momentum SGD (DmSGD), in which each node averages only with its neighbors, is more communication efficient than vanilla Parallel momentum SGD that incurs global average across all computing nodes. On the other hand, the large-batch training has been demonstrated critical to achieve runtime speedup. This motivates us to investigate how DmSGD performs in the large-batch scenario. In this work, we find the momentum term can amplify the inconsistency bias in DmSGD. Such bias becomes more evident …
Running Stochastic Gradient Descent (SGD) in a decentralized fashion has shown promising results. In this paper we propose Moniqua, a technique that allows decentralized SGD to use quantized communication. We prove in theory that Moniqua communicates a provably bounded number of bits per iteration, while converging at the same asymptotic rate as the original algorithm does with full-precision communication. Moniqua improves upon prior works in that it (1) requires zero additional memory, (2) works with 1-bit quantization, and (3) is applicable to a variety of decentralized algorithms. We demon…
Univ. Lille（里尔大学）；Inria（法国国家信息与自动化研究所）；CNRS（法国国家科学研究中心）；Centrale Lille（里尔中央理工学院）；Université de Bâle（巴塞尔大学）；EPFL（洛桑联邦理工学院）
One of the key challenges in decentralized and federated learning is to design algorithms that efficiently deal with highly heterogeneous data distributions across agents. In this paper, we revisit the analysis of the popular Decentralized Stochastic Gradient Descent algorithm (D-SGD) under data heterogeneity. We exhibit the key role played by a new quantity, called neighborhood heterogeneity, on the convergence rate of D-SGD. By coupling the communication topology and the heterogeneity, our analysis sheds light on the poorly understood interplay between these two concepts. We then argue that …
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…
We consider the decentralized stochastic optimization problems, where a network of $n$ nodes, each owning a local cost function, cooperate to find a minimizer of the globally-averaged cost. A widely studied decentralized algorithm for this problem is decentralized SGD (D-SGD), in which each node averages only with its neighbors. D-SGD is efficient in single-iteration communication, but it is very sensitive to the network topology. For smooth objective functions, the transient stage (which measures the number of iterations the algorithm has to experience before achieving the linear speedup stag…
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 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…
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…
Rutgers Business School（罗格斯商学院）；CNRS（法国国家科学研究中心）；INRIA（法国国家信息与自动化研究所）；DAMO Academy, Alibaba (US) Group（阿里巴巴（美国）集团达摩院）；Florida State University（佛罗里达州立大学）
Decentralized SGD and Average-direction SAM are Asymptotically Equivalent
College of Computer Science and Technology, Zhejiang University（浙江大学计算机科学与技术学院）；JD Explore Academy, JD.com, Inc.（京东探索研究院，京东集团）；Artificial Intelligence and its Applications Institute, School of Informatics, University of Edinburgh（爱丁堡大学信息学院人工智能及其应用研究所）；The University of Sydney（悉尼大学）
Zhejiang University（浙江大学）；The Pennsylvania State University（宾夕法尼亚州立大学）
We develop a general framework unifying several gradient-based stochastic optimization methods for empirical risk minimization problems both in centralized and distributed scenarios. The framework hinges on the introduction of an augmented graph consisting of nodes modeling the samples and edges modeling both the inter-device communication and intra-device stochastic gradient computation. By designing properly the topology of the augmented graph, we are able to recover as special cases the renowned Local-SGD and DSGD algorithms, and provide a unified perspective for variance-reduction (VR) and…
Emerging distributed applications recently boosted the development of decentralized machine learning, especially in IoT and edge computing fields. In real-world scenarios, the common problems of non-convexity and data heterogeneity result in inefficiency, performance degradation, and development stagnation. The bulk of studies concentrates on one of the issues mentioned above without having a more general framework that has been proven optimal. To this end, we propose a unified paradigm called UMP, which comprises two algorithms, D-SUM and GT-DSUM, based on the momentum technique with decentra…
University of California, Los Angeles（加利福尼亚大学洛杉矶分校）；Google Inc.（谷歌公司）；University of California, Santa Barbara（加利福尼亚大学圣巴巴拉分校）；DAMO Academy, Alibaba Group（阿里巴巴集团达摩院）
Decentralized SGD is an emerging training method for deep learning known for its much less (thus faster) communication per iteration, which relaxes the averaging step in parallel SGD to inexact averaging. The less exact the averaging is, however, the more the total iterations the training needs to take. Therefore, the key to making decentralized SGD efficient is to realize nearly-exact averaging using little communication. This requires a skillful choice of communication topology, which is an under-studied topic in decentralized optimization. In this paper, we study so-called exponential graph…
Yandex；HSE University（俄罗斯国立高等经济学院）；MIPT（莫斯科物理技术学院）；University of Toronto（多伦多大学）；Vector Institute
Training deep neural networks on large datasets can often be accelerated by using multiple compute nodes. This approach, known as distributed training, can utilize hundreds of computers via specialized message-passing protocols such as Ring All-Reduce. However, running these protocols at scale requires reliable high-speed networking that is only available in dedicated clusters. In contrast, many real-world applications, such as federated learning and cloud-based distributed training, operate on unreliable devices with unstable network bandwidth. As a result, these applications are restricted t…
We study the performance of decentralized stochastic gradient descent (DSGD) in a wireless network, where the nodes collaboratively optimize an objective function using their local datasets. Unlike the conventional setting, where the nodes communicate over error-free orthogonal communication links, we assume that transmissions are prone to additive noise and interference.We first consider a point-to-point (P2P) transmission strategy, termed the OAC-P2P scheme, in which the node pairs are scheduled in an orthogonal fashion to minimize interference. Since in the DSGD framework, each node require…
SOTA decentralized SGD algorithms can overcome the bandwidth bottleneck at the parameter server by using communication collectives like Ring All-Reduce for synchronization. While the parameter updates in distributed SGD may happen asynchronously there is still a synchronization barrier to make sure that the local training epoch at every learner is complete before the learners can advance to the next epoch. The delays in waiting for the slowest learners(stragglers) remain to be a problem in the synchronization steps of these state-of-the-art decentralized frameworks. In this paper, we propose t…
We consider the distributed learning problem where a network of $n$ agents seeks to minimize a global function $F$. Agents have access to $F$ through noisy gradients, and they can locally communicate with their neighbors a network. We study the Decentralized Local SDG method, where agents perform a number of local gradient steps and occasionally exchange information with their neighbors. Previous algorithmic analysis efforts have focused on the specific network topology (star topology) where a leader node aggregates all agents' information. We generalize that setting to an arbitrary network by…
Communication-efficient SGD algorithms, which allow nodes to perform local updates and periodically synchronize local models, are highly effective in improving the speed and scalability of distributed SGD. However, a rigorous convergence analysis and comparative study of different communication-reduction strategies remains a largely open problem. This paper presents a unified framework called Cooperative SGD that subsumes existing communication-efficient SGD algorithms such as periodic-averaging, elastic-averaging and decentralized SGD. By analyzing Cooperative SGD, we provide novel convergenc…
Topology-aware Generalization of Decentralized SGD
College of Computer Science and Technology, Zhejiang University（浙江大学计算机科学与技术学院）；Shanghai Institute for Advanced Study of Zhejiang University（浙江大学上海高等研究院）；JD Explore Academy, JD.com Inc.（京东探索研究院（京东））；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）；Institute of Artificial Intelligence, Hefei Comprehensive National Science Center（合肥综合性国家科学中心人工智能研究院）；School of Computer Science, Wuhan University（武汉大学计算机学院）；Zhejiang University City College（浙江大学城市学院）
Electronic Information School, Wuhan University（武汉大学）；Department of Electrical and Computer Engineering, North Carolina State University（北卡罗来纳州立大学）
While machine learning has achieved remarkable results in a wide variety of domains, the training of models often requires large datasets that may need to be collected from different individuals. As sensitive information may be contained in the individual's dataset, sharing training data may lead to severe privacy concerns. Therefore, there is a compelling need to develop privacy-aware machine learning methods, for which one effective approach is to leverage the generic framework of differential privacy. Considering that stochastic gradient descent (SGD) is one of the most commonly adopted met…
Temple University（天普大学）；University of Pittsburgh（匹兹堡大学）
Decentralized training has been actively studied in recent years. Although a wide variety of methods have been proposed, yet the decentralized momentum SGD method is still underexplored. In this paper, we propose a novel periodic decentralized momentum SGD method, which employs the momentum schema and periodic communication for decentralized training. With these two strategies, as well as the topology of the decentralized training system, the theoretical convergence analysis of our proposed method is difficult. We address this challenging problem and provide the condition under which our propo…
DSGD-CECA: Decentralized SGD with Communication-Optimal Exact Consensus Algorithm
University of California, Los Angeles（加州大学洛杉矶分校）；Princeton University（普林斯顿大学）；Google Inc.（谷歌公司）；Peking University（北京大学）；AI for Science Institute（科学智能研究院）；Alibaba US（阿里巴巴美国公司）
Decentralized Parallel SGD (D-PSGD) and its asynchronous variant Asynchronous Parallel SGD (AD-PSGD) is a family of distributed learning algorithms that have been demonstrated to perform well for large-scale deep learning tasks. One drawback of (A)D-PSGD is that the spectral gap of the mixing matrix decreases when the number of learners in the system increases, which hampers convergence. In this paper, we investigate techniques to accelerate (A)D-PSGD based training by improving the spectral gap while minimizing the communication cost. We demonstrate the effectiveness of our proposed technique…
IIIT-Delhi（德里英迪拉甘地信息技术学院）；Czech Technical University in Prague（布拉格捷克理工大学）
Powered by the simplicity of lock-free asynchrony, Hogwilld! is a go-to approach to parallelize SGD over a shared-memory setting. Despite its popularity and concomitant extensions, such as PASSM+ wherein concurrent processes update a shared model with partitioned gradients, scaling it to decentralized workers has surprisingly been relatively unexplored. To our knowledge, there is no convergence theory of such methods, nor systematic numerical comparisons evaluating speed-up. In this paper, we propose an algorithm incorporating decentralized distributed memory computing architecture with each n…
We consider decentralized stochastic optimization with the objective function (e.g. data samples for machine learning task) being distributed over $n$ machines that can only communicate to their neighbors on a fixed communication graph. To reduce the communication bottleneck, the nodes compress (e.g. quantize or sparsify) their model updates. We cover both unbiased and biased compression operators with quality denoted by $ω\leq 1$ ($ω=1$ meaning no compression). We (i) propose a novel gossip-based stochastic gradient descent algorithm, CHOCO-SGD, that converges at rate $\mathcal{O}\left(1/(nT)…
Temple University（天普大学）；University of Pittsburgh（匹兹堡大学）
With the emergence of distributed data, training machine learning models in the serverless manner has attracted increasing attention in recent years. Numerous training approaches have been proposed in this regime, such as decentralized SGD. However, all existing decentralized algorithms only focus on standard SGD. It might not be suitable for some applications, such as deep factorization machine in which the feature is highly sparse and categorical so that the adaptive training algorithm is needed. In this paper, we propose a novel adaptive decentralized training approach, which can compute th…
College of Computer, National University of Defense Technology（国防科技大学计算机学院）；Scientific Computing & Imaging Institute, University of Utah（犹他大学科学计算与成像研究所）
The stability and generalization of stochastic gradient-based methods provide valuable insights into understanding the algorithmic performance of machine learning models. As the main workhorse for deep learning, stochastic gradient descent has received a considerable amount of studies. Nevertheless, the community paid little attention to its decentralized variants. In this paper, we provide a novel formulation of the decentralized stochastic gradient descent. Leveraging this formulation together with (non)convex optimization theory, we establish the first stability and generalization guarantee…
The University of Queensland（昆士兰大学）；Griffith University（格里菲斯大学）；Monash University（莫纳什大学）
Actuated by the growing attention to personal healthcare and the pandemic, the popularity of E-health is proliferating. Nowadays, enhancement on medical diagnosis via machine learning models has been highly effective in many aspects of e-health analytics. Nevertheless, in the classic cloud-based/centralized e-health paradigms, all the data will be centrally stored on the server to facilitate model training, which inevitably incurs privacy concerns and high time delay. Distributed solutions like Decentralized Stochastic Gradient Descent (D-SGD) are proposed to provide safe and timely diagnostic…
Carnegie Mellon University（卡内基梅隆大学）；Facebook AI Research（脸书人工智能研究院）
Distributed optimization is essential for training large models on large datasets. Multiple approaches have been proposed to reduce the communication overhead in distributed training, such as synchronizing only after performing multiple local SGD steps, and decentralized methods (e.g., using gossip algorithms) to decouple communications among workers. Although these methods run faster than AllReduce-based methods, which use blocking communication before every update, the resulting models may be less accurate after the same number of updates. Inspired by the BMUF method of Chen & Huo (2016), we…
In this paper, we study decentralized online stochastic non-convex optimization over a network of nodes. Integrating a technique called gradient tracking in decentralized stochastic gradient descent, we show that the resulting algorithm, GT-DSGD, enjoys certain desirable characteristics towards minimizing a sum of smooth non-convex functions. In particular, for general smooth non-convex functions, we establish non-asymptotic characterizations of GT-DSGD and derive the conditions under which it achieves network-independent performances that match the centralized minibatch SGD. In contrast, the …
Decentralized training of deep learning models is a key element for enabling data privacy and on-device learning over networks, as well as for efficient scaling to large compute clusters. As current approaches suffer from limited bandwidth of the network, we propose the use of communication compression in the decentralized training context. We show that Choco-SGD $-$ recently introduced and analyzed for strongly-convex objectives only $-$ converges under arbitrary high compression ratio on general non-convex functions at the rate $O\bigl(1/\sqrt{nT}\bigr)$ where $T$ denotes the number of itera…
RIKEN Center for Emergent Matter Science (CEMS)（理化学研究所新兴物质科学中心）；The University of Tokyo（东京大学）；University of Tokyo（东京大学）
Recent studies have demonstrated that noise in stochastic gradient descent (SGD) is closely related to generalization: A larger SGD noise, if not too large, results in better generalization. Since the covariance of the SGD noise is proportional to $η^2/B$, where $η$ is the learning rate and $B$ is the minibatch size of SGD, the SGD noise has so far been controlled by changing $η$ and/or $B$. However, too large $η$ results in instability in the training dynamics and a small $B$ prevents scalable parallel computation. It is thus desirable to develop a method of controlling the SGD noise without …
