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 for e.g. by means of reducing the precision of compressed information. In particular, we show that having $O(\log\frac{1}ε)$ gradient iterations {with constant step size} - and $O(\log\frac{1}ε)$ gossip steps between every pair of these iterations - enables convergence to within $ε$ of the optimal value for smooth non-convex objectives satisfying Polyak-Łojasiewicz condition. This result also holds for smooth strongly convex objectives. To our knowledge, this is the first work that derives convergence results for nonconvex optimization under arbitrary communication compression.
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)…
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 …
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）
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…
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…
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…
Communication overhead hinders the scalability of large-scale distributed training. Gossip SGD, where each node averages only with its neighbors, is more communication-efficient than the prevalent parallel SGD. However, its convergence rate is reversely proportional to quantity $1-β$ which measures the network connectivity. On large and sparse networks where $1-β\to 0$, Gossip SGD requires more iterations to converge, which offsets against its communication benefit. This paper introduces Gossip-PGA, which adds Periodic Global Averaging into Gossip SGD. Its transient stage, i.e., the iterations…
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…
Inria（法国国家信息与自动化研究所）；PSL Research University（巴黎文理研究大学）；Ecole Polytechnique Fédérale de Lausanne（洛桑联邦理工学院）；Univ. Grenoble Alpes（格勒诺布尔阿尔卑斯大学）；CNRS（法国国家科学研究中心）；Grenoble INP（格勒诺布尔理工学院）；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）
We introduce the continuized Nesterov acceleration, a close variant of Nesterov acceleration whose variables are indexed by a continuous time parameter. The two variables continuously mix following a linear ordinary differential equation and take gradient steps at random times. This continuized variant benefits from the best of the continuous and the discrete frameworks: as a continuous process, one can use differential calculus to analyze convergence and obtain analytical expressions for the parameters; and a discretization of the continuized process can be computed exactly with convergence r…
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…
Accelerated Gossip via Stochastic Heavy Ball Method
School of Mathematics, KAUST, Saudi Arabia（卡士塔大学数学学院，沙特阿拉伯）；The University of Edinburgh（爱丁堡大学）；The University of Edinburgh, United Kingdom（英国爱丁堡大学）；Edinburgh, Scotland, UK（苏格兰爱丁堡，英国）；MIPT, Russia（莫斯科国立信息安全大学，俄罗斯）
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…
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…
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）
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…
National University of Defense Technology（国防科技大学）；University of Rochester（罗切斯特大学）；Tencent AI Lab（腾讯人工智能实验室）
Decentralized Online Learning (online learning in decentralized networks) attracts more and more attention, since it is believed that Decentralized Online Learning can help the data providers cooperatively better solve their online problems without sharing their private data to a third party or other providers. Typically, the cooperation is achieved by letting the data providers exchange their models between neighbors, e.g., recommendation model. However, the best regret bound for a decentralized online learning algorithm is $\Ocal{n\sqrt{T}}$, where $n$ is the number of nodes (or users) and $…
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）
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）
Byzantine-Robust Gossip: Insights from a Dual Approach
Center for Applied Mathematics（应用数学中心）；École polytechnique（巴黎高等理工学院）；IP Paris Palaiseau（巴黎-Palaiseau研究所）；Inria（法国国家信息与自动化技术研究所）；Center of Grenoble Alpes University（格勒诺布尔阿尔卑斯大学中心）；CNRS, LJK（国家科学研究中心，LJK）
Decentralized Online Convex Optimization with Unknown Feedback Delays
Università degli Studi di Milano（米兰大学）；University of Iowa（爱荷华大学）；Université de Lille（里尔大学）；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）；Centrale Lille（里尔中央理工学院）
Decentralized stochastic optimization has recently benefited from gradient tracking methods \cite{DSGT_Pu,DSGT_Xin} providing efficient solutions for large-scale empirical risk minimization problems. In Part I \cite{GT_SAGA} of this work, we develop \textbf{\texttt{GT-SAGA}} that is based on a decentralized implementation of SAGA \cite{SAGA} using gradient tracking and discuss regimes of practical interest where \textbf{\texttt{GT-SAGA}} outperforms existing decentralized approaches in terms of the total number of local gradient computations. In this paper, we describe \textbf{\texttt{GT-SVRG}…
LAYUP: Asynchronous decentralized gradient descent with LAYer-wise UPdates
Center for Cognitive Interaction Technology, Universität Bielefeld, Germany（认知交互技术中心，比勒菲尔德大学，德国）；Bielefeld University（比勒菲尔德大学）；Department of Computer Science, Royal Holloway, University of London, United Kingdom（计算机科学系，伦敦大学皇家霍洛威学院，英国）
Kyoto University（京都大学）；RIKEN AIP（理化学研究所先进智能项目中心）；NTT Communication Science Laboratories（NTT通信科学实验室）
In decentralized learning, operator splitting methods using a primal-dual formulation (e.g., the Edge-Consensus Learning (ECL)) has been shown to be robust to heterogeneous data and has attracted significant attention in recent years. However, in the ECL, a node needs to exchange dual variables with its neighbors. These exchanges incur significant communication costs. For the Gossip-based algorithms, many compression methods have been proposed, but these Gossip-based algorithm do not perform well when the data distribution held by each node is statistically heterogeneous. In this work, we prop…
Decentralized learning enables edge users to collaboratively train models by exchanging information via device-to-device communication, yet prior works have been limited to wireless networks with fixed topologies and reliable workers. In this work, we propose an asynchronous decentralized stochastic gradient descent (DSGD) algorithm, which is robust to the inherent computation and communication failures occurring at the wireless network edge. We theoretically analyze its performance and establish a non-asymptotic convergence guarantee. Experimental results corroborate our analysis, demonstrati…
