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distributed and communication-efficient solutions to linear equations with special sparse structure

SYSTEMS & CONTROL LETTERS 2022年 160卷 105065-105065页

作者： Wang, Peng Gao, Yuanqi Yu, Nanpeng Ren, Wei Lian, Jianming Wu, Di Shanghai Jiao Tong Univ Dept Automat Shanghai 200240 Peoples R China Minist Educ China Key Lab Syst Control & Informat Proc Shanghai 200240 Peoples R China Shanghai Engn Res Ctr Intelligent Control & Manage Shanghai 200240 Peoples R China Univ Calif Riverside 900 Univ Ave Riverside CA 92521 USA Oak Ridge Natl Lab 1 Bethel Valley Rd Oak Ridge TN 37831 USA Pacific Northwest Natl Lab 902 Battelle Blvd Richland WA 99354 USA

In this paper, two distributed and communication-efficient algorithms based on the multi-agent system are proposed to solve a system of linear equations with the Laplacian sparse system matrix. One algorithm is based on the gradient descent method in optimization. In this algorithm, the agents only share partial information instead of all of their collective state vectors to save significant communication. The other algorithm is obtained by approximating Newton's method for a faster convergence rate. Although it requires twice as much communication as the first one, it is still communication-efficient given the low dimension of the information shared among agents. The convergence at a linear rate is proved for both algorithms, and a comprehensive comparison of their convergence rate, communication burden, and computation costs is also performed. The proposed algorithms can be applied to various systems to solve those problems that can be modeled as a system of linear equations with a Laplacian sparse system matrix. Simulation results with the electric power system illustrate their effectiveness. (C)& nbsp;2021 Published by Elsevier B.V.

关键词： distributed method Multi-agent system Linear equations Power system

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distributed Minimum Error Entropy Algorithms

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JOURNAL OF MACHINE LEARNING RESEARCH 2020年第1期21卷 1-31页

作者： Guo, Xin Hu, Ting Wu, Qiang Hong Kong Polytech Univ Dept Appl Math Hong Kong Peoples R China Univ Queensland Sch Math & Phys Brisbane Qld 4072 Australia Wuhan Univ Sch Math & Stat Wuhan 430072 Peoples R China Middle Tennessee State Univ Dept Math Sci Murfreesboro TN 37132 USA

Minimum Error Entropy (MEE) principle is an important approach in Information Theoretical Learning (ITL). It is widely applied and studied in various fields for its robustness to noise. In this paper, we study a reproducing kernel-based distributed MEE algorithm, DMEE, which is designed to work with both fully supervised data and semi-supervised data. The divide-and-conquer approach is employed, so there is no inter-node communication overhead. Similar as other distributed algorithms, DMEE significantly reduces the computational complexity and memory requirement on single computing nodes. With fully supervised data, our proved learning rates equal the minimax optimal learning rates of the classical pointwise kernel-based regressions. Under the semi-supervised learning scenarios, we show that DMEE exploits unlabeled data effectively, in the sense that first, under the settings with weak regularity assumptions, additional unlabeled data significantly improves the learning rates of DMEE. Second, with sufficient unlabeled data, labeled data can be distributed to many more computing nodes, that each node takes only O(1) labels, without spoiling the learning rates in terms of the number of labels. This conclusion overcomes the saturation phenomenon in unlabeled data size. It parallels a recent results for regularized least squares (Lin and Zhou, 2018), and suggests that an inflation of unlabeled data is a solution to the MEE learning problems with decentralized data source for the concerns of privacy protection. Our work refers to pairwise learning and non-convex loss. The theoretical analysis is achieved by distributed U-statistics and error decomposition techniques in integral operators.

关键词： Information theoretic learning minimum error entropy distributed method semi-supervised data reproducing kernel Hilbert space

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Coordinated optimal dispatch of VPPs in unbalanced ADNs

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IET GENERATION TRANSMISSION & DISTRIBUTION 2020年第8期14卷 1430-1437页

作者： Xu, Tong Wu, Wenchuan Wang, Zhen-Yi Zhu, Tao Tsinghua Univ Tsinghua Berkeley Shenzhen Inst Shenzhen Environm Sci & New Energy Technol Engn L Shenzhen Peoples R China Tsinghua Univ Dept Elect Engn State Key Lab Power Syst Beijing Peoples R China Yunnan Power Grid Co Ltd Power Dispatch & Control Ctr Kunming Yunnan Peoples R China Kunming Elect Power Supply Bur Power Dispatch & Control Ctr Kunming Yunnan Peoples R China

To manage and control massive distributed energy resources (DERs) integrated into active distribution networks (ADNs), dispersed DERs are aggregated as virtual power plants (VPPs). This study introduces a distributed optimal dispatch strategy of VPPs considering operational constraints in unbalanced ADN. First, a practical multi-VPP coordination optimal dispatch model considering P-Q coupling characteristics in unbalanced ADN is proposed. Then, the primal-dual interior-point algorithm is employed to transform the original model into a Karush-Kuhn-Tucker equation, where afterwards distributed quasi-Newton method is developed to solve the equation. Under the proposed distributed strategy, each VPP only communicates limited boundary information with utility grid. With the advantage of quasi-second-order information, the proposed method outperforms the popular distributed gradient-based algorithm, alternating direction method of multipliers. The distributed method provides merits such as efficient calculation and privacy protection for multi-VPP operation in ADN. Numerical tests evaluate the efficiency and accuracy of the proposed method.

关键词： Newton method energy resources distributed power generation power grids distribution networks power generation dispatch nonlinear programming power system management power plants primal-dual interior-point algorithm distributed quasiNewton method quasisecond-order information distributed method VPP unbalanced ADN massive distributed energy resources active distribution networks virtual power plants distributed optimal dispatch strategy multiVPP coordination optimal dispatch model dispersed DER Karush-Kuhn-Tucker equation DER management DER control operational constraints P-Q coupling characteristics privacy protection

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Accelerated Multi-Agent Optimization method over Stochastic Networks 59

Accelerated Multi-Agent Optimization Method over Stochastic ...

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59th IEEE Conference on Decision and Control (CDC)

作者： Ananduta, Wicak Ocampo-Martinez, Carlos Nedic, Angelia Delft Univ Technol Delft Ctr Syst & Control DCSC Delft Netherlands Inst Robot & Informat Ind CSIC UPC Barcelona Spain Arizona State Univ Sch Elect Comp & Energy Engn Tempe AZ 85287 USA

ISBN: (纸本)9781728174471

We propose a distributed method to solve a multi-agent optimization problem with strongly convex cost function and equality coupling constraints. The method is based on Nesterov's accelerated gradient approach and works over stochastically time-varying communication networks. We consider the standard assumptions of Nesterov's method and show that the sequence of the expected dual values converge toward the optimal value with the rate of O(1/k(2)). Furthermore, we provide a simulation study of solving an optimal power flow problem with a well-known benchmark case.

关键词： multi-agent optimization distributed method accelerated gradient method distributed optimal power flow problem

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Penalty methods for distributed Optimization with Inequality and Equality Constraints

Penalty Methods for Distributed Optimization with Inequality...

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第40届中国控制会议

作者： Zicong Xia Yang Liu College of Mathematics and Computer Science Zhejiang Normal University

This paper focuses on the penalty method, which has the potential to turn constrained problems into unconstrained ones, for distributed optimization with inequality and equality constraints. A selection principle to choose penalty gains is proposed based on value-distance ratio. Furthermore, a distributed method is developed to solve the obtained problems while its convergence is rigorously proved. Finally, an example in a numerical way demonstrates the validity of this paper.

关键词： distributed optimization Penalty methods distributed method Non-smooth analysis

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distributed pairwise algorithms with gradient descent methods

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NEUROCOMPUTING 2019年 333卷 364-373页

作者： Wang, Baobin Hu, Ting South Cent Univ Nationalities Sch Math & Stat Wuhan 430074 Hubei Peoples R China Wuhan Univ Sch Math & Stat Wuhan 430072 Hubei Peoples R China

Pairwise algorithms refer to a learning problem with loss functions depending on pairs of examples. There has been remarkable work on analyzing their generalization properties in batch and online settings such as algorithmic stabilities, robustness or regularization. This paper is concerned with distributed pairwise algorithms for dealing with big data, based on a divide-and-conquer strategy. We show that the global estimator of the distributed pairwise algorithm is as good as that of the classical algorithm processing the whole data on a single machine. We present the optimal convergence rate for the distributed pairwise algorithm and provide a theoretical upper bound for the number of local machines under which the optimal rate is retained. Our analysis is achieved by the integral operator decomposition and distributed U-statistics. (C) 2019 Elsevier B.V. All rights reserved.

关键词： distributed method Pairwise algorithms Gradient descent Reproducing kernel Hilbert spaces

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Fully distributed AC power flow (ACPF) algorithm for distribution systems

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IET SMART GRID 2019年第2期2卷 155-162页

作者： Pourbabak, Hajir Ajao, Adetokunbo Chen, Tao Su, Wencong Univ Michigan Coll Engn & Comp Sci Dept Elect & Comp Engn Dearborn MI 48128 USA

Power flow is one of the basic tools for system operation and control. Due to its nature, which determines the complex nodal voltages, line flows, currents and losses, it enforces a large computation load on a power system. A distributed/decentralised algorithm unburdens the central controller and shares the total computation load with all agents. Therefore, such algorithms are an effective method for dealing with power flow complexity. In this study, a distributed method based on a linearised AC power system is proposed. First, the linearisation procedure of a comprehensive non-linear AC power flow (ACPF) is detailed. Second, a distributed method is presented based upon the linear ACPF equations. Three case studies are presented to evaluate the overall performance of the proposed method. In the first case study, the accuracy level of both linearised ACPF and distributed ACPF is assessed. In the second case study, the dynamic performance of distributed ACPF is investigated based on the load sudden changes. In the third case study, the scalability of the proposed distributed ACPF is evaluated by applying it to a larger power system.

关键词： load flow power system security power system management AC power flow algorithm distribution systems system operation control complex nodal voltages distributed decentralised algorithm central controller shares total computation load effective method power flow complexity distributed method linearised AC power system nonlinear AC power flow linear ACPF equations case study linearised ACPF distributed ACPF larger power system

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Research on distributed Autonomous Time Reference Maintain method of Navigation Constellation 8th

Research on Distributed Autonomous Time Reference Maintain M...

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8th China Satellite Navigation Conference (CSNC)

作者： Yang, Daoning Li, Gang Liu, Ying Yang, Jun Meng, Yinan Zhang, Xianyu Natl Univ Def Technol Coll Mechatron Engn & Automat Changsha 410073 Hunan Peoples R China Beijing Inst Tracking & Telecommun Technol Beijing 100094 Peoples R China Rocket Force Acad Beijing 100000 Peoples R China

ISBN: (纸本)9789811045943;9789811045936

Satellite navigation system to provide users with high-precision positioning, navigation, and timing services, requires a uniform high-precision time reference. When the navigation system is operating in the normal mode, this reference is maintained by the ground and measured through the satellite-ground link and modifies the onboard clock parameters to ensure the uniformity of the entire system time reference. In the autonomous navigation mode, the navigation constellation to leave the ground support, need to maintain the time reference autonomously. This paper analyzes the maintenance method of autonomous time reference based on inter-satellite observation and designs a distributed autonomous time reference maintenance algorithm. The satellite clock error is used as the basic observation to compose the system measurement equation. According to the system state equation, each satellite uses Kalman filter to estimate and update its own clock parameters to maintain the constellation time reference. Simulation results show that the proposed algorithm can maintain the uniform time reference of navigation constellations.

关键词： Inter-satellite link Time reference GNSS distributed method

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distributed minimum error entropy algorithms

The Journal of Machine Learning Research

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The Journal of Machine Learning Research 2020年第1期21卷 4968-4998页

作者： Xin Guo Ting Hu Qiang Wu Department of Applied Mathematics The Hong Kong Polytechnic University Hong Kong China and School of Mathematics and Physics The University of Queensland Brisbane QLD Australia School of Mathematics and Statistics Wuhan University Wuhan China Department of Mathematical Sciences Middle Tennessee State University Murfreesboro TN

Minimum Error Entropy (MEE) principle is an important approach in Information Theoretical Learning (ITL). It is widely applied and studied in various fields for its robustness to noise. In this paper, we study a reproducing kernel-based distributed MEE algorithm, DMEE, which is designed to work with both fully supervised data and semi-supervised data. The divide-and-conquer approach is employed, so there is no inter-node communication overhead. Similar as other distributed algorithms, DMEE significantly reduces the computational complexity and memory requirement on single computing nodes. With fully supervised data, our proved learning rates equal the minimax optimal learning rates of the classical pointwise kernel-based regressions. Under the semi-supervised learning scenarios, we show that DMEE exploits unlabeled data effectively, in the sense that first, under the settings with weak regularity assumptions, additional unlabeled data significantly improves the learning rates of DMEE. Second, with su_cient unlabeled data, labeled data can be distributed to many more computing nodes, that each node takes only O(1) labels, without spoiling the learning rates in terms of the number of labels. This conclusion overcomes the saturation phenomenon in unlabeled data size. It parallels a recent results for regularized least squares (Lin and Zhou, 2018), and suggests that an ination of unlabeled data is a solution to the MEE learning problems with decentralized data source for the concerns of privacy protection. Our work refers to pairwise learning and non-convex loss. The theoretical analysis is achieved by distributed U-statistics and error decomposition techniques in integral operators.

关键词： information theoretic learning minimum error entropy distributed method semi-supervised data reproducing kernel Hilbert space

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A Fully distributed method to Detect and Reduce Cut Vertices in Large-Scale Overlay Networks

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IEEE TRANSACTIONS ON COMPUTERS 2012年第7期61卷 969-985页

作者： Liu, Xiaomei Xiao, Li Kreling, Andrew Texas Commiss Environm Qual Informat Resource Div Austin TX 78726 USA Michigan State Univ Dept Comp Sci & Engn E Lansing MI 48824 USA Google Inc Mountain View CA 94043 USA

A cut vertex is defined as a network node whose removal increases the number of network components. Failure of a cut vertex disconnects a network component and downgrades the network performance. Overlay networks are resilient to the failure of random nodes, but cut vertices that have been observed in real-world overlay traces make the network very vulnerable to well-constructed and targeted attacks. Traditional methods of detecting cut vertices are centralized and are very difficult, if not impossible, to be applied to large-scale and highly dynamic overlay networks. We aim to provide a practical solution by proposing a distributed mechanism that detects the cut vertices and neutralizes them to noncut vertices before they fail. The proposed mechanism not only minimizes the possibility of network decomposition on the cut vertex failure but also offloads the traffic that is handled by the cut vertices. We prove that our proposed method can correctly identify the cut vertices. We evaluate the performance of our design through trace-driven simulations. The results show that our method can successfully locate all cut vertices in the network and greatly offload the traffic processed by cut vertices.

关键词： Overlay network cut vertex distributed method reliability accuracy

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