Beyond spectral gap (extended): The role of the topology in decentralized learning
EPFL（洛桑联邦理工学院）
Thijs Vogels, Hadrien Hendrikx, Martin Jaggi
备注：
Extended version of the other paper (with the same name), that includes (among other things) theory for the heterogeneous case. arXiv admin note: substantial text overlap with arXiv:2206.03093
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 prescribes smaller learning rates, which further decrease as graphs become larger, failing to explain convergence dynamics in infinite graphs. This paper aims to paint an accurate picture of sparsely-connected distributed optimization. We quantify how the graph topology influences convergence in a quadratic toy problem and provide theoretical results for general smooth and (strongly) convex objectives. Our theory matches empirical observations in deep learning, and accurately describes the relative merits of different graph topologies. This paper is an extension of the conference paper by Vogels et. al. (2022). Code: https://github.com/epfml/topology-in-decentralized-learning.
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…
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…
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…
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…
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…
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 …
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…
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…
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）
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…
Recently, local peer topology has been shown to influence the overall convergence of decentralized learning (DL) graphs in the presence of data heterogeneity. In this paper, we demonstrate the advantages of constructing a proxy-based locally heterogeneous DL topology to enhance convergence and maintain data privacy. In particular, we propose a novel peer clumping strategy to efficiently cluster peers before arranging them in a final training graph. By showing how locally heterogeneous graphs outperform locally homogeneous graphs of similar size and from the same global data distribution, we pr…
By leveraging deep learning based technologies, the data-driven based approaches have reached great success with the rapid increase of data generated of Industrial Indernet of Things(IIot). However, security and privacy concerns are obstacles for data providers in many sensitive data-driven industrial scenarios, such as healthcare and auto-driving. Many Federated Learning(FL) approaches have been proposed with DNNs for IIoT applications, these works still suffer from low usability of data due to data incompleteness, low quality, insufficient quantity, sensitivity, etc. Therefore, we propose a …
Topology-Independent Robustness of the Weighted Mean under Label Poisoning Attacks in Heterogeneous Decentralized Learning
School of Computer Science and Engineering, Sun Yat-Sen University（中山大学计算机科学与工程学院）；School of Engineering and Applied Science, Harvard University（哈佛大学工程与应用科学学院）；Department of Electrical and Electronic Engineering, Imperial College London（伦敦帝国理工学院电子与电气工程系）
Topology Learning for Heterogeneous Decentralized Federated Learning over Unreliable D2D Networks
School of Computer Science and Technology, Harbin Institute of Technology Shenzhen（哈尔滨工业大学（深圳）计算机科学与技术学院）；University of Electronic Science and Technology of China（电子科技大学）
Department of Computer, Control and Management Engineering, Sapienza University of Rome（罗马萨皮恩扎大学计算机、控制与管理工程系）；Department of Computer Science, Sapienza University of Rome（罗马萨皮恩扎大学计算机科学系）；Università della Svizzera Italiana（意大利瑞士大学）
A recent emphasis of distributed learning research has been on federated learning (FL), in which model training is conducted by the data-collecting devices. Existing research on FL has mostly focused on a star topology learning architecture with synchronized (time-triggered) model training rounds, where the local models of the devices are periodically aggregated by a centralized coordinating node. However, in many settings, such a coordinating node may not exist, motivating efforts to fully decentralize FL. In this work, we propose a novel methodology for distributed model aggregations via asy…
Decentralized Bilevel Optimization: A Perspective from Transient Iteration Complexity
Center for Data Science, Peking University（北京大学数据科学中心）；Center for Machine Learning Research, Peking University AI for Science Institute（北京大学人工智能科学研究院机器学习研究中心）
Towards Heterogeneity-Aware and Energy-Efficient Topology Optimization for Decentralized Federated Learning in Edge Environment
School of Engineering, Swinburne University of Technology（工程学院，斯威本科技大学）；School of Computer Science and Technology, Tongji University（计算机科学与技术学院，同济大学）；State Key Lab for Novel Software Technology, Nanjing University（新型软件技术国家重点实验室，南京大学）；School of Computer Science and Artificial Intelligence, Wuhan University of Technology（计算机科学与人工智能学院，武汉科技大学）；School of Cyber Science and Engineering, Wuhan University（网络科学与工程学院，武汉大学）；CSIRO Data61
We consider the decentralized exploration problem: a set of players collaborate to identify the best arm by asynchronously interacting with the same stochastic environment. The objective is to insure privacy in the best arm identification problem between asynchronous, collaborative, and thrifty players. In the context of a digital service, we advocate that this decentralized approach allows a good balance between the interests of users and those of service providers: the providers optimize their services, while protecting the privacy of the users and saving resources. We define the privacy lev…
Learning Decentralized Traffic Signal Controllers with Multi-Agent Graph Reinforcement Learning
Northwestern Polytechnical University（西北工业大学）；Harbin Engineering University（哈尔滨工程大学）；Hong Kong University of Science and Technology（香港科技大学）；Xidian University（西安电子科技大学）；Nanyang Technological University（南洋理工大学）
DAMO Academy, Alibaba Group（阿里巴巴集团达摩院）；Peking University（北京大学）；University of Pennsylvania（宾夕法尼亚大学）；MetaCarbon
Decentralized optimization is effective to save communication in large-scale machine learning. Although numerous algorithms have been proposed with theoretical guarantees and empirical successes, the performance limits in decentralized optimization, especially the influence of network topology and its associated weight matrix on the optimal convergence rate, have not been fully understood. While (Lu and Sa, 2021) have recently provided an optimal rate for non-convex stochastic decentralized optimization with weight matrices defined over linear graphs, the optimal rate with general weight matri…
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…
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…
Decentralized optimization methods enable on-device training of machine learning models without a central coordinator. In many scenarios communication between devices is energy demanding and time consuming and forms the bottleneck of the entire system. We propose a new randomized first-order method which tackles the communication bottleneck by applying randomized compression operators to the communicated messages. By combining our scheme with a new variance reduction technique that progressively throughout the iterations reduces the adverse effect of the injected quantization noise, we obtain …
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）
We study decentralized non-convex finite-sum minimization problems described over a network of nodes, where each node possesses a local batch of data samples. In this context, we analyze a single-timescale randomized incremental gradient method, called GT-SAGA. GT-SAGA is computationally efficient as it evaluates one component gradient per node per iteration and achieves provably fast and robust performance by leveraging node-level variance reduction and network-level gradient tracking. For general smooth non-convex problems, we show the almost sure and mean-squared convergence of GT-SAGA to a…
King Abdullah University of Science and Technology（阿卜杜拉国王科技大学）；Moscow Institute of Physics and Technology（莫斯科物理技术学院）
We propose ADOM - an accelerated method for smooth and strongly convex decentralized optimization over time-varying networks. ADOM uses a dual oracle, i.e., we assume access to the gradient of the Fenchel conjugate of the individual loss functions. Up to a constant factor, which depends on the network structure only, its communication complexity is the same as that of accelerated Nesterov gradient method (Nesterov, 2003). To the best of our knowledge, only the algorithm of Rogozin et al. (2019) has a convergence rate with similar properties. However, their algorithm converges under the very re…
The University of Iowa（爱荷华大学）；IBM T. J. Watson Research Center（IBM托马斯·J·沃森研究中心）
Generative Adversarial Networks (GANs) are a powerful class of generative models in the deep learning community. Current practice on large-scale GAN training utilizes large models and distributed large-batch training strategies, and is implemented on deep learning frameworks (e.g., TensorFlow, PyTorch, etc.) designed in a centralized manner. In the centralized network topology, every worker needs to either directly communicate with the central node or indirectly communicate with all other workers in every iteration. However, when the network bandwidth is low or network latency is high, the per…
Tokyo University of Science（东京理科大学）；Tsuda University（津田塾大学）
This paper proposes a communication strategy for decentralized learning on wireless systems. Our discussion is based on the decentralized parallel stochastic gradient descent (D-PSGD), which is one of the state-of-the-art algorithms for decentralized learning. The main contribution of this paper is to raise a novel open question for decentralized learning on wireless systems: there is a possibility that the density of a network topology significantly influences the runtime performance of D-PSGD. In general, it is difficult to guarantee delay-free communications without any communication deteri…
UiT The Arctic University of Norway（挪威北极大学）；NORCE Norwegian Research Centre AS（NORCE挪威研究中心公司）
We propose an end-to-end framework based on a Graph Neural Network (GNN) to balance the power flows in energy grids. The balancing is framed as a supervised vertex regression task, where the GNN is trained to predict the current and power injections at each grid branch that yield a power flow balance. By representing the power grid as a line graph with branches as vertices, we can train a GNN that is accurate and robust to changes in topology. In addition, by using specialized GNN layers, we are able to build a very deep architecture that accounts for large neighborhoods on the graph, while im…
DFed-SST: Building Semantic- and Structure-aware Topologies for Decentralized Federated Graph Learning
Shandong University, School of Mechanical, Electrical and Information Engineering（山东大学，机械电子信息工程学院）；Beijing Institute of Technology, School of Computer Science and Technology（北京理工大学，计算机科学与技术学院）；Sun Yat-sen University, School of Computer Science and Engineering（中山大学，计算机科学与工程学院）
There is significant recent interest to parallelize deep learning algorithms in order to handle the enormous growth in data and model sizes. While most advances focus on model parallelization and engaging multiple computing agents via using a central parameter server, aspect of data parallelization along with decentralized computation has not been explored sufficiently. In this context, this paper presents a new consensus-based distributed SGD (CDSGD) (and its momentum variant, CDMSGD) algorithm for collaborative deep learning over fixed topology networks that enables data parallelization as w…
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…
IIT Kanpur（印度理工学院坎普尔分校）；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）
Decentralized learning provides an effective framework to train machine learning models with data distributed over arbitrary communication graphs. However, most existing approaches toward decentralized learning disregard the interaction between data heterogeneity and graph topology. In this paper, we characterize the dependence of convergence on the relationship between the mixing weights of the graph and the data heterogeneity across nodes. We propose a metric that quantifies the ability of a graph to mix the current gradients. We further prove that the metric controls the convergence rate, p…
Carnegie Mellon University（卡内基梅隆大学）；King Abdullah University of Science and Technology（阿卜杜拉国王科技大学）
Emerging applications in multi-agent environments such as internet-of-things, networked sensing, autonomous systems and federated learning, call for decentralized algorithms for finite-sum optimizations that are resource-efficient in terms of both computation and communication. In this paper, we consider the prototypical setting where the agents work collaboratively to minimize the sum of local loss functions by only communicating with their neighbors over a predetermined network topology. We develop a new algorithm, called DEcentralized STochastic REcurSive gradient methodS (DESTRESS) for non…
Princeton University（普林斯顿大学）；Carnegie Mellon University（卡内基梅隆大学）；King Abdullah University of Science and Technology（阿卜杜拉国王科技大学）
Communication efficiency has been widely recognized as the bottleneck for large-scale decentralized machine learning applications in multi-agent or federated environments. To tackle the communication bottleneck, there have been many efforts to design communication-compressed algorithms for decentralized nonconvex optimization, where the clients are only allowed to communicate a small amount of quantized information (aka bits) with their neighbors over a predefined graph topology. Despite significant efforts, the state-of-the-art algorithm in the nonconvex setting still suffers from a slower ra…
