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 $\mathcal{O}\left(1/(nT) + 1/(T δ^2 ω)^2\right)$ for strongly convex objectives, where $T$ denotes the number of iterations and $δ$ the eigengap of the connectivity matrix. Despite compression quality and network connectivity affecting the higher order terms, the first term in the rate, $\mathcal{O}(1/(nT))$, is the same as for the centralized baseline with exact communication. We (ii) present a novel gossip algorithm, CHOCO-GOSSIP, for the average consensus problem that converges in time $\mathcal{O}(1/(δ^2ω) \log (1/ε))$ for accuracy $ε> 0$. This is (up to our knowledge) the first gossip algorithm that supports arbitrary compressed messages for $ω> 0$ and still exhibits linear convergence. We (iii) show in experiments that both of our algorithms do outperform the respective state-of-the-art baselines and CHOCO-SGD can reduce communication by at least two orders of magnitudes.
University of Texas at Austin（得克萨斯大学奥斯汀分校）；Amazon（亚马逊）
In decentralized optimization, it is common algorithmic practice to have nodes interleave (local) gradient descent iterations with gossip (i.e. averaging over the network) steps. Motivated by the training of large-scale machine learning models, it is also increasingly common to require that messages be {\em lossy compressed} versions of the local parameters. In this paper, we show that, in such compressed decentralized optimization settings, there are benefits to having {\em multiple} gossip steps between subsequent gradient iterations, even when the cost of doing so is appropriately accounted…
Distributed learning has become an integral tool for scaling up machine learning and addressing the growing need for data privacy. Although more robust to the network topology, decentralized learning schemes have not gained the same level of popularity as their centralized counterparts for being less competitive performance-wise. In this work, we attribute this issue to the lack of synchronization among decentralized learning workers, showing both empirically and theoretically that the convergence rate is tied to the synchronization level among the workers. Such motivated, we present a novel d…
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.
Sorbonne Universités（索邦大学）；UPMC Univ Paris 06（巴黎第六大学）；ENSEA（法国高等电力学院）；Université Cergy-Pontoise（塞尔吉-蓬图瓦兹大学）；CNRS（法国国家科学研究中心）
We address the issue of speeding up the training of convolutional networks. Here we study a distributed method adapted to stochastic gradient descent (SGD). The parallel optimization setup uses several threads, each applying individual gradient descents on a local variable. We propose a new way to share information between different threads inspired by gossip algorithms and showing good consensus convergence properties. Our method called GoSGD has the advantage to be fully asynchronous and decentralized. We compared our method to the recent EASGD in \cite{elastic} on CIFAR-10 show encouraging …
This paper considers decentralized optimization with application to machine learning on graphs. The growing size of neural network (NN) models has motivated prior works on decentralized stochastic gradient algorithms to incorporate communication compression. On the other hand, recent works have demonstrated the favorable convergence and generalization properties of overparameterized NNs. In this work, we present an empirical analysis on the performance of compressed decentralized stochastic gradient (DSG) algorithms with overparameterized NNs. Through simulations on an MPI network environment,…
Unveiling the Power of Multiple Gossip Steps: A Stability-Based Generalization Analysis in Decentralized Training
State Key Laboratory of Digital Intelligent Modeling and Simulation（数字智能建模与仿真国家重点实验室）；National University of Defense Technology（国防科技大学）；School of Cyber Science and Technology（网络安全科学与技术学院）；Shenzhen Campus of Sun Yat-sen University（中山大学深圳校区）
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…
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…
Decentralization is a promising method of scaling up parallel machine learning systems. In this paper, we provide a tight lower bound on the iteration complexity for such methods in a stochastic non-convex setting. Our lower bound reveals a theoretical gap in known convergence rates of many existing decentralized training algorithms, such as D-PSGD. We prove by construction this lower bound is tight and achievable. Motivated by our insights, we further propose DeTAG, a practical gossip-style decentralized algorithm that achieves the lower bound with only a logarithm gap. Empirically, we compar…
Kyoto University（京都大学）；RIKEN AIP（理化学研究所人工智能研究中心）；NTT Communication Science Laboratories（NTT通信科学实验室）
In recent years, decentralized learning has emerged as a powerful tool not only for large-scale machine learning, but also for preserving privacy. One of the key challenges in decentralized learning is that the data distribution held by each node is statistically heterogeneous. To address this challenge, the primal-dual algorithm called the Edge-Consensus Learning (ECL) was proposed and was experimentally shown to be robust to the heterogeneity of data distributions. However, the convergence rate of the ECL is provided only when the objective function is convex, and has not been shown in a sta…
Compressed Decentralized Momentum Stochastic Gradient Methods for Nonconvex Optimization
Department of Mathematical Sciences（数学科学系）；Rensselaer Polytechnic Institute（伦斯勒理工学院）；Department of Computer Science（计算机科学系）；MIT-IBM Watson AI Lab, IBM Research（MIT-IBM Watson AI实验室，IBM研究）；IBM T. J. Watson Research Center（IBM T.J. 华生研究中心）
EPFL（洛桑联邦理工学院）；Mila（米拉研究所）；DIRO, Université de Montréal（蒙特利尔大学信息与运筹学系）
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 convergen…
Compressed Gradient Tracking for Decentralized Optimization Over General Directed Networks
Shanghai Center for Mathematical Sciences, Fudan University（复旦大学上海数学中心）；Shenzhen Research Institute of Big Data（深圳大数据研究院）；School of Data Science, The Chinese University of Hong Kong, Shenzhen（香港中文大学（深圳）数据科学学院）；Department of Mathematics, Michigan State University（密歇根州立大学数学系）
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…
Revisiting Decentralized Online Convex Optimization with Compressed Communication
School of Software Technology, Zhejiang University（浙江大学软件学院）；State Key Laboratory of Blockchain and Data Security, Zhejiang University（浙江大学区块链与数据安全全国重点实验室）
Bilevel optimization have gained growing interests, with numerous applications found in meta learning, minimax games, reinforcement learning, and nested composition optimization. This paper studies the problem of distributed bilevel optimization over a network where agents can only communicate with neighbors, including examples from multi-task, multi-agent learning and federated learning. In this paper, we propose a gossip-based distributed bilevel learning algorithm that allows networked agents to solve both the inner and outer optimization problems in a single timescale and share information…
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）
INRIA（法国国家信息与自动化研究所）；Ecole normale supérieure（巴黎高等师范学院）；CNRS（法国国家科学研究中心）；PSL Research University（巴黎文理研究大学）；MSR-INRIA Joint Centre（微软研究院-法国国家信息与自动化研究所联合中心）
In this paper, we study the problem of minimizing a sum of smooth and strongly convex functions split over the nodes of a network in a decentralized fashion. We propose the algorithm $ESDACD$, a decentralized accelerated algorithm that only requires local synchrony. Its rate depends on the condition number $κ$ of the local functions as well as the network topology and delays. Under mild assumptions on the topology of the graph, $ESDACD$ takes a time $O((τ_{\max} + Δ_{\max})\sqrt{κ/γ}\ln(ε^{-1}))$ to reach a precision $ε$ where $γ$ is the spectral gap of the graph, $τ_{\max}$ the maximum commun…
The emerging concern about data privacy and security has motivated the proposal of federated learning, which allows nodes to only synchronize the locally-trained models instead their own original data. Conventional federated learning architecture, inherited from the parameter server design, relies on highly centralized topologies and the assumption of large nodes-to-server bandwidths. However, in real-world federated learning scenarios the network capacities between nodes are highly uniformly distributed and smaller than that in a datacenter. It is of great challenges for conventional federate…
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…
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…
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…
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）；Université de 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）；Inria, Univ Montpellier（法国国家信息与自动化研究所、蒙彼利埃大学）
We study the decentralized consensus and stochastic optimization problems with compressed communications over static directed graphs. We propose an iterative gradient-based algorithm that compresses messages according to a desired compression ratio. The proposed method provably reduces the communication overhead on the network at every communication round. Contrary to existing literature, we allow for arbitrary compression ratios in the communicated messages. We show a linear convergence rate for the proposed method on the consensus problem. Moreover, we provide explicit convergence rates for …
Decentralized Federated Anomaly Detection in Smart Grids: A P2P Gossip Approach
Centre for Cyber Resilience and Trust (CREST), Deakin University（网络弹性与信任中心（CREST），迪肯大学）；Department of Computer Science & IT, Latrobe University（计算机科学与信息技术系，拉筹伯大学）
Decentralized learning algorithms empower interconnected devices to share data and computational resources to collaboratively train a machine learning model without the aid of a central coordinator. In the case of heterogeneous data distributions at the network nodes, collaboration can yield predictors with unsatisfactory performance for a subset of the devices. For this reason, in this work, we consider the formulation of a distributionally robust decentralized learning task and we propose a decentralized single loop gradient descent/ascent algorithm (AD-GDA) to directly solve the underlying …
University of Illinois at Urbana-Champaign（伊利诺伊大学厄巴纳-香槟分校）
Compressed Stochastic Gradient Descent (SGD) algorithms have been recently proposed to address the communication bottleneck in distributed and decentralized optimization problems, such as those that arise in federated machine learning. Existing compressed SGD algorithms assume the use of non-adaptive step-sizes(constant or diminishing) to provide theoretical convergence guarantees. Typically, the step-sizes are fine-tuned in practice to the dataset and the learning algorithm to provide good empirical performance. Such fine-tuning might be impractical in many learning scenarios, and it is there…
