Consensus-based distributed optimization methods have recently been advocated as alternatives to parameter server and ring all-reduce paradigms for large scale training of machine learning models. In this case, each worker maintains a local estimate of the optimal parameter vector and iteratively updates it by averaging the estimates obtained from its neighbors, and applying a correction on the basis of its local dataset. While theoretical results suggest that worker communication topology should have strong impact on the number of epochs needed to converge, previous experiments have shown the opposite conclusion. This paper sheds lights on this apparent contradiction and show how sparse topologies can lead to faster convergence even in the absence of communication delays.
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…
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 …
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…
University of Rochester（罗切斯特大学）；ETH Zurich（苏黎世联邦理工学院）；University of California, Davis（加利福尼亚大学戴维斯分校）；IBM T. J. Watson Research Center（IBM托马斯·J·沃森研究中心）；Tencent AI lab（腾讯人工智能实验室）
Most distributed machine learning systems nowadays, including TensorFlow and CNTK, are built in a centralized fashion. One bottleneck of centralized algorithms lies on high communication cost on the central node. Motivated by this, we ask, can decentralized algorithms be faster than its centralized counterpart? Although decentralized PSGD (D-PSGD) algorithms have been studied by the control community, existing analysis and theory do not show any advantage over centralized PSGD (C-PSGD) algorithms, simply assuming the application scenario where only the decentralized network is available. In th…
In data-parallel optimization of machine learning models, workers collaborate to improve their estimates of the model: more accurate gradients allow them to use larger learning rates and optimize faster. In the decentralized setting, in which workers communicate over a sparse graph, current theory fails to capture important aspects of real-world behavior. First, the `spectral gap' of the communication graph is not predictive of its empirical performance in (deep) learning. Second, current theory does not explain that collaboration enables larger learning rates than training alone. In fact, it …
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…
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,…
In data-parallel optimization of machine learning models, workers collaborate to improve their estimates of the model: more accurate gradients allow them to use larger learning rates and optimize faster. We consider the setting in which all workers sample from the same dataset, and communicate over a sparse graph (decentralized). In this setting, current theory fails to capture important aspects of real-world behavior. First, the 'spectral gap' of the communication graph is not predictive of its empirical performance in (deep) learning. Second, current theory does not explain that collaboratio…
University of California, Santa Barbara（加州大学圣巴巴拉分校）；University of Texas at Austin（得克萨斯大学奥斯汀分校）；University of Pennsylvania（宾夕法尼亚大学）
We consider the problem of decentralized consensus optimization, where the sum of $n$ smooth and strongly convex functions are minimized over $n$ distributed agents that form a connected network. In particular, we consider the case that the communicated local decision variables among nodes are quantized in order to alleviate the communication bottleneck in distributed optimization. We propose the Quantized Decentralized Gradient Descent (QDGD) algorithm, in which nodes update their local decision variables by combining the quantized information received from their neighbors with their local in…
Decentralized methods to solve finite-sum minimization problems are important in many signal processing and machine learning tasks where the data is distributed over a network of nodes and raw data sharing is not permitted due to privacy and/or resource constraints. In this article, we review decentralized stochastic first-order methods and provide a unified algorithmic framework that combines variance-reduction with gradient tracking to achieve both robust performance and fast convergence. We provide explicit theoretical guarantees of the corresponding methods when the objective functions are…
In this work, we introduce an asynchronous decentralized accelerated stochastic gradient descent type of method for decentralized stochastic optimization, considering communication and synchronization are the major bottlenecks. We establish $\mathcal{O}(1/ε)$ (resp., $\mathcal{O}(1/\sqrtε)$) communication complexity and $\mathcal{O}(1/ε^2)$ (resp., $\mathcal{O}(1/ε)$) sampling complexity for solving general convex (resp., strongly convex) problems.
University of Minnesota Twin Cities（明尼苏达大学双城分校）；IBM Research AI（IBM研究院AI）；IBM Thomas J. Watson Research Center（IBM托马斯·J·沃森研究中心）
Many modern large-scale machine learning problems benefit from decentralized and stochastic optimization. Recent works have shown that utilizing both decentralized computing and local stochastic gradient estimates can outperform state-of-the-art centralized algorithms, in applications involving highly non-convex problems, such as training deep neural networks. In this work, we propose a decentralized stochastic algorithm to deal with certain smooth non-convex problems where there are $m$ nodes in the system, and each node has a large number of samples (denoted as $n$). Differently from the maj…
Iowa State University（爱荷华州立大学）；Johnson Controls（江森自控）；New York University（纽约大学）
We consider the problem of decentralized deep learning where multiple agents collaborate to learn from a distributed dataset. While there exist several decentralized deep learning approaches, the majority consider a central parameter-server topology for aggregating the model parameters from the agents. However, such a topology may be inapplicable in networked systems such as ad-hoc mobile networks, field robotics, and power network systems where direct communication with the central parameter server may be inefficient. In this context, we propose and analyze a novel decentralized deep learning…
Decentralized stochastic gradient method emerges as a promising solution for solving large-scale machine learning problems. This paper studies the decentralized Markov chain gradient descent (DMGD) algorithm - a variant of the decentralized stochastic gradient methods where the random samples are taken along the trajectory of a Markov chain. This setting is well-motivated when obtaining independent samples is costly or impossible, which excludes the use of the traditional stochastic gradient algorithms. Specifically, we consider the first- and zeroth-order versions of decentralized Markov chai…
Rutgers Business School（罗格斯大学商学院）；The Chinese University of Hong Kong（香港中文大学）；Florida State University（佛罗里达州立大学）
Stochastic gradient Langevin dynamics (SGLD) and stochastic gradient Hamiltonian Monte Carlo (SGHMC) are two popular Markov Chain Monte Carlo (MCMC) algorithms for Bayesian inference that can scale to large datasets, allowing to sample from the posterior distribution of the parameters of a statistical model given the input data and the prior distribution over the model parameters. However, these algorithms do not apply to the decentralized learning setting, when a network of agents are working collaboratively to learn the parameters of a statistical model without sharing their individual data …
The convergence speed of machine learning models trained with Federated Learning is significantly affected by heterogeneous data partitions, even more so in a fully decentralized setting without a central server. In this paper, we show that the impact of label distribution skew, an important type of data heterogeneity, can be significantly reduced by carefully designing the underlying communication topology. We present D-Cliques, a novel topology that reduces gradient bias by grouping nodes in sparsely interconnected cliques such that the label distribution in a clique is representative of the…
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}…
University of Toronto（多伦多大学）；Westlake University（西湖大学）；EPFL（洛桑联邦理工学院）；CISPA Helmholtz Center for Information Security（亥姆霍兹信息安全中心）
Gradient tracking (GT) is an algorithm designed for solving decentralized optimization problems over a network (such as training a machine learning model). A key feature of GT is a tracking mechanism that allows to overcome data heterogeneity between nodes. We develop a novel decentralized tracking mechanism, $K$-GT, that enables communication-efficient local updates in GT while inheriting the data-independence property of GT. We prove a convergence rate for $K$-GT on smooth non-convex functions and prove that it reduces the communication overhead asymptotically by a linear factor $K$, where $…
Decentralized solutions to finite-sum minimization are of significant importance in many signal processing, control, and machine learning applications. In such settings, the data is distributed over a network of arbitrarily-connected nodes and raw data sharing is prohibitive often due to communication or privacy constraints. In this article, we review decentralized stochastic first-order optimization methods and illustrate some recent improvements based on gradient tracking and variance reduction, focusing particularly on smooth and strongly-convex objective functions. We provide intuitive ill…
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…
In this paper, we design Top-DP, a novel solution to optimize the differential privacy protection of decentralized image classification systems. The key insight of our solution is to leverage the unique features of decentralized communication topologies to reduce the noise scale and improve the model usability. (1) We enhance the DP-SGD algorithm with this topology-aware noise reduction strategy, and integrate the time-aware noise decay technique. (2) We design two novel learning protocols (synchronous and asynchronous) to protect systems with different network connectivities and topologies. W…
Decentralized Nonconvex Composite Federated Learning with Gradient Tracking and Momentum
School of Cyber Science & Engineering, Southeast University（东南大学网络空间科学与工程学院）；Institute of Artificial Intelligence (TeleAI) of China Telecom（中国电信人工智能研究院）；School of Mathematics, Southeast University（东南大学数学学院）；Purple Mountain Laboratories（紫金山实验室）
Adaptive gradient methods including Adam, AdaGrad, and their variants have been very successful for training deep learning models, such as neural networks. Meanwhile, given the need for distributed computing, distributed optimization algorithms are rapidly becoming a focal point. With the growth of computing power and the need for using machine learning models on mobile devices, the communication cost of distributed training algorithms needs careful consideration. In this paper, we introduce novel convergent decentralized adaptive gradient methods and rigorously incorporate adaptive gradient m…
Iowa State University（爱荷华州立大学）；Johnson Controls（江森自控）；New York University（纽约大学）
Decentralized learning enables a group of collaborative agents to learn models using a distributed dataset without the need for a central parameter server. Recently, decentralized learning algorithms have demonstrated state-of-the-art results on benchmark data sets, comparable with centralized algorithms. However, the key assumption to achieve competitive performance is that the data is independently and identically distributed (IID) among the agents which, in real-life applications, is often not applicable. Inspired by ideas from continual learning, we propose Cross-Gradient Aggregation (CGA)…
Decentralized learning over distributed datasets can have significantly different data distributions across the agents. The current state-of-the-art decentralized algorithms mostly assume the data distributions to be Independent and Identically Distributed. This paper focuses on improving decentralized learning over non-IID data. We propose \textit{Neighborhood Gradient Clustering (NGC)}, a novel decentralized learning algorithm that modifies the local gradients of each agent using self- and cross-gradient information. Cross-gradients for a pair of neighboring agents are the derivatives of the…
LoDAdaC: a unified local training-based decentralized framework with adaptive gradients and compressed communication
Rensselaer Polytechnic Institute（伦斯勒理工学院）；IBM T. J. Watson Research Center（IBM T. J. Watson 研究中心）；MIT-IBM Watson AI Lab, IBM Research（MIT-IBM Watson AI 实验室，IBM 研究院）
Michigan State University（密歇根州立大学）；Princeton University（普林斯顿大学）
This paper proposes a novel proximal-gradient algorithm for a decentralized optimization problem with a composite objective containing smooth and non-smooth terms. Specifically, the smooth and nonsmooth terms are dealt with by gradient and proximal updates, respectively. The proposed algorithm is closely related to a previous algorithm, PG-EXTRA \cite{shi2015proximal}, but has a few advantages. First of all, agents use uncoordinated step-sizes, and the stable upper bounds on step-sizes are independent of network topologies. The step-sizes depend on local objective functions, and they can be as…
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）
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…
Distributed descent-based methods are an essential toolset to solving optimization problems in multi-agent system scenarios. Here the agents seek to optimize a global objective function through mutual cooperation. Oftentimes, cooperation is achieved over a wireless communication network that is prone to delays and errors. There are many scenarios wherein the objective function is either non-differentiable or merely observable. In this paper, we present a cross-entropy based distributed stochastic approximation algorithm (SA) that finds a minimum of the objective, using only samples. We call th…
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…
Fudan University（复旦大学）；Tsinghua University（清华大学）；Beijing National Research Center for Information Science and Technology（北京信息科学与技术国家研究中心）；The Chinese University of Hong Kong（香港中文大学）
In decentralized learning, a network of nodes cooperate to minimize an overall objective function that is usually the finite-sum of their local objectives, and incorporates a non-smooth regularization term for the better generalization ability. Decentralized stochastic proximal gradient (DSPG) method is commonly used to train this type of learning models, while the convergence rate is retarded by the variance of stochastic gradients. In this paper, we propose a novel algorithm, namely DPSVRG, to accelerate the decentralized training by leveraging the variance reduction technique. The basic ide…
This paper considers decentralized stochastic optimization over a network of $n$ nodes, where each node possesses a smooth non-convex local cost function and the goal of the networked nodes is to find an $ε$-accurate first-order stationary point of the sum of the local costs. We focus on an online setting, where each node accesses its local cost only by means of a stochastic first-order oracle that returns a noisy version of the exact gradient. In this context, we propose a novel single-loop decentralized hybrid variance-reduced stochastic gradient method, called GT-HSGD, that outperforms the …
Xi’an Jiaotong University（西安交通大学）；Fudan University（复旦大学）；The Hong Kong Polytechnic University（香港理工大学）；The Hong Kong University of Science and Technology（香港科技大学）
From Models to Network Topologies: A Topology Inference Attack in Decentralized Federated Learning
Communication Systems Group, Department of Informatics, University of Zurich, CH--8050 Zürich, Switzerland（苏黎世大学信息学院通信系统组）；Department of Information and Communications Engineering, University of Murcia, 30100--Murcia, Spain（穆尔西亚大学信息与通信工程系）
Massachusetts General Hospital（麻省总医院）；Harvard Medical School（哈佛医学院）；Harvard University（哈佛大学）；Beijing International Center for Mathematical Research（北京国际数学研究中心）；Peking University（北京大学）；School of Engineering and Applied Science, Harvard University（哈佛大学工程与应用科学学院）
With a computationally efficient approximation of the second-order information, natural gradient methods have been successful in solving large-scale structured optimization problems. We study the natural gradient methods for the large-scale decentralized optimization problems on Riemannian manifolds, where the local objective function defined by the local dataset is of a log-probability type. By utilizing the structure of the Riemannian Fisher information matrix (RFIM), we present an efficient decentralized Riemannian natural gradient descent (DRNGD) method. To overcome the communication issue…
Department of Computer Science, University of Rochester（罗切斯特大学计算机科学系）；Department of Computational Mathematics, Science and Engineering, Michigan State University（密歇根州立大学计算数学、科学与工程系）；Department of Computer Science, ETH Zurich（苏黎世联邦理工学院计算机科学系）；Tencent AI Lab（腾讯AI实验室）
While training a machine learning model using multiple workers, each of which collects data from their own data sources, it would be most useful when the data collected from different workers can be {\em unique} and {\em different}. Ironically, recent analysis of decentralized parallel stochastic gradient descent (D-PSGD) relies on the assumption that the data hosted on different workers are {\em not too different}. In this paper, we ask the question: {\em Can we design a decentralized parallel stochastic gradient descent algorithm that is less sensitive to the data variance across workers?} I…
Georgia Institute of Technology（佐治亚理工学院）；Virginia Tech（弗吉尼亚理工大学）
We develop a mathematical framework for solving multi-task reinforcement learning (MTRL) problems based on a type of policy gradient method. The goal in MTRL is to learn a common policy that operates effectively in different environments; these environments have similar (or overlapping) state spaces, but have different rewards and dynamics. We highlight two fundamental challenges in MTRL that are not present in its single task counterpart, and illustrate them with simple examples. We then develop a decentralized entropy-regularized policy gradient method for solving the MTRL problem, and study…
Texas A&M University（德克萨斯农工大学）；University of Minnesota（明尼苏达大学）
We consider a distributed non-convex optimization where a network of agents aims at minimizing a global function over the Stiefel manifold. The global function is represented as a finite sum of smooth local functions, where each local function is associated with one agent and agents communicate with each other over an undirected connected graph. The problem is non-convex as local functions are possibly non-convex (but smooth) and the Steifel manifold is a non-convex set. We present a decentralized Riemannian stochastic gradient method (DRSGD) with the convergence rate of $\mathcal{O}(1/\sqrt{K…
