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 rate of convergence $O((G/T)^{2/3})$ compared with their uncompressed counterpart, where $G$ measures the data heterogeneity across different clients, and $T$ is the number of communication rounds. This paper proposes BEER, which adopts communication compression with gradient tracking, and shows it converges at a faster rate of $O(1/T)$. This significantly improves over the state-of-the-art rate, by matching the rate without compression even under arbitrary data heterogeneity. Numerical experiments are also provided to corroborate our theory and confirm the practical superiority of BEER in the data heterogeneous regime.
University of Science and Technology of China（中国科学技术大学）；Infinia ML, Inc.（Infinia ML公司）
Decentralized optimization algorithms have attracted intensive interests recently, as it has a balanced communication pattern, especially when solving large-scale machine learning problems. Stochastic Path Integrated Differential Estimator Stochastic First-Order method (SPIDER-SFO) nearly achieves the algorithmic lower bound in certain regimes for nonconvex problems. However, whether we can find a decentralized algorithm which achieves a similar convergence rate to SPIDER-SFO is still unclear. To tackle this problem, we propose a decentralized variant of SPIDER-SFO, called decentralized SPIDER…
Department of Industrial and Systems Engineering, Lehigh University（利哈伊大学工业与系统工程系）
The beer game is a widely used in-class game that is played in supply chain management classes to demonstrate the bullwhip effect. The game is a decentralized, multi-agent, cooperative problem that can be modeled as a serial supply chain network in which agents cooperatively attempt to minimize the total cost of the network even though each agent can only observe its own local information. Each agent chooses order quantities to replenish its stock. Under some conditions, a base-stock replenishment policy is known to be optimal. However, in a decentralized supply chain in which some agents (sta…
Clemson University（克莱姆森大学）；University of Illinois at Urbana-Champaign（伊利诺伊大学厄巴纳-香槟分校）
Privacy protection and nonconvexity are two challenging problems in decentralized optimization and learning involving sensitive data. Despite some recent advances addressing each of the two problems separately, no results have been reported that have theoretical guarantees on both privacy protection and saddle/maximum avoidance in decentralized nonconvex optimization. We propose a new algorithm for decentralized nonconvex optimization that can enable both rigorous differential privacy and saddle/maximum avoiding performance. The new algorithm allows the incorporation of persistent additive noi…
The minimax optimization over Riemannian manifolds (possibly nonconvex constraints) has been actively applied to solve many problems, such as robust dimensionality reduction and deep neural networks with orthogonal weights (Stiefel manifold). Although many optimization algorithms for minimax problems have been developed in the Euclidean setting, it is difficult to convert them into Riemannian cases, and algorithms for nonconvex minimax problems with nonconvex constraints are even rare. On the other hand, to address the big data challenges, decentralized (serverless) training techniques have re…
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…
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）
Convergence of Decentralized Stochastic Subgradient-based Methods for Nonsmooth Nonconvex functions
State Key Laboratory of Scientific and Engineering Computing, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, and University of Chinese Academy of Sciences, China（国家科学工程计算重点实验室，数学系统科学学院，中国科学院，中国科学院大学）
École Polytechnique Fédérale de Lausanne（洛桑联邦理工学院）
Rapid advances in data collection and processing capabilities have allowed for the use of increasingly complex models that give rise to nonconvex optimization problems. These formulations, however, can be arbitrarily difficult to solve in general, in the sense that even simply verifying that a given point is a local minimum can be NP-hard [1]. Still, some relatively simple algorithms have been shown to lead to surprisingly good empirical results in many contexts of interest. Perhaps the most prominent example is the success of the backpropagation algorithm for training neural networks. Several…
An Efficient Stochastic Algorithm for Decentralized Nonconvex-Strongly-Concave Minimax Optimization
SGIT AI Lab, State Grid Corporation of China（国网公司SGIT AI实验室）；School of Data Science, Fudan University（复旦大学数据科学学院）；Shanghai Key Laboratory for Contemporary Applied Mathematics（上海市现代应用数学重点实验室）
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）
College of Computer Science and Technology, Nanjing University of Aeronautics and Astronautics（南京航空航天大学计算机科学与技术学院）；MIIT Key Laboratory of Pattern Analysis and Machine Intelligence（工业和信息化部模式分析与机器智能重点实验室）
We study Byzantine collaborative learning, where $n$ nodes seek to collectively learn from each others' local data. The data distribution may vary from one node to another. No node is trusted, and $f < n$ nodes can behave arbitrarily. We prove that collaborative learning is equivalent to a new form of agreement, which we call averaging agreement. In this problem, nodes start each with an initial vector and seek to approximately agree on a common vector, which is close to the average of honest nodes' initial vectors. We present two asynchronous solutions to averaging agreement, each we prove op…
Iowa State University（爱荷华州立大学）；The Ohio State University（俄亥俄州立大学）；Air Force Research Laboratory（空军研究实验室）
Decentralized nonconvex optimization has received increasing attention in recent years in machine learning due to its advantages in system robustness, data privacy, and implementation simplicity. However, three fundamental challenges in designing decentralized optimization algorithms are how to reduce their sample, communication, and memory complexities. In this paper, we propose a \underline{g}radient-\underline{t}racking-based \underline{sto}chastic \underline{r}ecursive \underline{m}omentum (GT-STORM) algorithm for efficiently solving nonconvex optimization problems. We show that to reach a…
On the Complexity of Decentralized Smooth Nonconvex Finite-Sum Optimization
School of Data Science, Fudan University（复旦大学数据科学学院）；Siebel School of Computing and Data Science, University of Illinois Urbana-Champaign（伊利诺伊大学厄巴纳-香槟分校西贝尔计算与数据科学学院）
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…
Purdue University（普渡大学）；University of Rome “La Sapienza”（罗马第一大学）；U.S. Army Research Laboratory（美国陆军研究实验室）
This paper studies Dictionary Learning problems wherein the learning task is distributed over a multi-agent network, modeled as a time-varying directed graph. This formulation is relevant, for instance, in Big Data scenarios where massive amounts of data are collected/stored in different locations (e.g., sensors, clouds) and aggregating and/or processing all data in a fusion center might be inefficient or unfeasible, due to resource limitations, communication overheads or privacy issues. We develop a unified decentralized algorithmic framework for this class of nonconvex problems, which is pro…
Distributed machine learning algorithms enable learning of models from datasets that are distributed over a network without gathering the data at a centralized location. While efficient distributed algorithms have been developed under the assumption of faultless networks, failures that can render these algorithms nonfunctional occur frequently in the real world. This paper focuses on the problem of Byzantine failures, which are the hardest to safeguard against in distributed algorithms. While Byzantine fault tolerance has a rich history, existing work does not translate into efficient and prac…
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…
Decentralized algorithms for stochastic optimization and learning rely on the diffusion of information as a result of repeated local exchanges of intermediate estimates. Such structures are particularly appealing in situations where agents may be hesitant to share raw data due to privacy concerns. Nevertheless, in the absence of additional privacy-preserving mechanisms, the exchange of local estimates, which are generated based on private data can allow for the inference of the data itself. The most common mechanism for guaranteeing privacy is the addition of perturbations to local estimates b…
Computational Science Initiative（计算科学计划）；Brookhaven National Laboratory（布鲁克海文国家实验室）
This work examines the convergence of stochastic gradient-based optimization algorithms that use early stopping based on a validation function. The form of early stopping we consider is that optimization terminates when the norm of the gradient of a validation function falls below a threshold. We derive conditions that guarantee this stopping rule is well-defined, and provide bounds on the expected number of iterations and gradient evaluations needed to meet this criterion. The guarantee accounts for the distance between the training and validation sets, measured with the Wasserstein distance.…
A Variance-Reduced Stochastic Gradient Tracking Algorithm for Decentralized Optimization with Orthogonality Constraints
State Key Laboratory of Scientific and Engineering Computing, Academy of Mathematics and Systems Science, Chinese Academy of Sciences（中国科学院数学与系统科学研究院科学与工程计算国家重点实验室）；University of Chinese Academy of Sciences（中国科学院大学）
Nonconvex sparse learning plays an essential role in many areas, such as signal processing and deep network compression. Iterative hard thresholding (IHT) methods are the state-of-the-art for nonconvex sparse learning due to their capability of recovering true support and scalability with large datasets. Theoretical analysis of IHT is currently based on centralized IID data. In realistic large-scale situations, however, data are distributed, hardly IID, and private to local edge computing devices. It is thus necessary to examine the property of IHT in federated settings, which update in parall…
The Ohio State University（俄亥俄州立大学）；Iowa State University（爱荷华州立大学）；University of Minnesota（明尼苏达大学）；IBM Thomas J. Watson Research Center（IBM托马斯·J·沃森研究中心）
In recent years, decentralized bilevel optimization problems have received increasing attention in the networking and machine learning communities thanks to their versatility in modeling decentralized learning problems over peer-to-peer networks (e.g., multi-agent meta-learning, multi-agent reinforcement learning, personalized training, and Byzantine-resilient learning). However, for decentralized bilevel optimization over peer-to-peer networks with limited computation and communication capabilities, how to achieve low sample and communication complexities are two fundamental challenges that r…
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…
Federated learning allows loads of edge computing devices to collaboratively learn a global model without data sharing. The analysis with partial device participation under non-IID and unbalanced data reflects more reality. In this work, we propose federated learning versions of adaptive gradient methods - Federated AGMs - which employ both the first-order and second-order momenta, to alleviate generalization performance deterioration caused by dissimilarity of data population among devices. To further improve the test performance, we compare several schemes of calibration for the adaptive lea…
The Ohio State University（俄亥俄州立大学）；Iowa State University（爱荷华州立大学）；IBM Research AI（IBM人工智能研究院）
Recently, min-max optimization problems have received increasing attention due to their wide range of applications in machine learning (ML). However, most existing min-max solution techniques are either single-machine or distributed algorithms coordinated by a central server. In this paper, we focus on the decentralized min-max optimization for learning with domain constraints, where multiple agents collectively solve a nonconvex-strongly-concave min-max saddle point problem without coordination from any server. Decentralized min-max optimization problems with domain constraints underpins many…
Huazhong University of Science and Technology（华中科技大学）；University of Waterloo（滑铁卢大学）；Northeastern University（东北大学）；KTH Royal Institute of Technology（瑞典皇家理工学院）
Traditional machine learning relies on a centralized data pipeline, i.e., data are provided to a central server for model training. In many applications, however, data are inherently fragmented. Such a decentralized nature of these databases presents the biggest challenge for collaboration: sending all decentralized datasets to a central server raises serious privacy concerns. Although there has been a joint effort in tackling such a critical issue by proposing privacy-preserving machine learning frameworks, such as federated learning, most state-of-the-art frameworks are built still in a cent…
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…
Argonne National Laboratory（阿贡国家实验室）；Wayne State University（韦恩州立大学）
In distributed machine learning, efficient training across multiple agents with different data distributions poses significant challenges. Even with a centralized coordinator, current algorithms that achieve optimal communication complexity typically require either large minibatches or compromise on gradient complexity. In this work, we tackle both centralized and decentralized settings across strongly convex, convex, and nonconvex objectives. We first demonstrate that a basic primal-dual method, (Accelerated) Gradient Ascent Multiple Stochastic Gradient Descent (GA-MSGD), applied to the Lagra…
On the Trade-off between Flatness and Optimization in Distributed Learning
Institute of Electrical and Micro Engineering in EPFL（瑞士联邦理工学院电气与微电子工程学院）；Sun Yat-sen University（中山大学）；Center for Machine Learning Research (CMLR) in Peking University（北京大学机器学习研究中心）
Temple University（天普大学）；MBZUAI（穆罕默德·本·扎耶德人工智能大学）；University of Florida（佛罗里达大学）
Bilevel optimization has been applied to a wide variety of machine learning models, and numerous stochastic bilevel optimization algorithms have been developed in recent years. However, most existing algorithms restrict their focus on the single-machine setting so that they are incapable of handling the distributed data. To address this issue, under the setting where all participants compose a network and perform peer-to-peer communication in this network, we developed two novel decentralized stochastic bilevel optimization algorithms based on the gradient tracking communication mechanism and …
The University of Sydney（悉尼大学）；Queen’s University Belfast（贝尔法斯特女王大学）；Federation University（联邦大学）；University of Newcastle（纽卡斯尔大学）
Non-Independent and Identically Distributed (non- IID) data distribution among clients is considered as the key factor that degrades the performance of federated learning (FL). Several approaches to handle non-IID data such as personalized FL and federated multi-task learning (FMTL) are of great interest to research communities. In this work, first, we formulate the FMTL problem using Laplacian regularization to explicitly leverage the relationships among the models of clients for multi-task learning. Then, we introduce a new view of the FMTL problem, which in the first time shows that the for…
Federated learning with heavy-tailed gradient noise and communication noise: a variance-reduction based algorithm
School of Mathematics, China University of Mining and Technology（中国矿业大学数学学院）；School of Mathematical Sciences, Dalian University of Technology（大连理工大学数学科学学院）
