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Stochastic sub-gradient algorithm for distributed optimization with random sleep scheme

控制理论与技术（英文版） 2015年第4期13卷 333-347页

作者： Peng YI Yiguang HONG Key Lab of Systems and Control Academy of Mathematics and Systems Science Chinese Academy of Sciences Beijing 100190 China

In this paper, we consider a distributed convex optimization problem of a multi-agent system with the global objective function as the sum of agents’ individual objective functions. To solve such an optimization problem, we propose a distributed stochastic sub-gradient algorithm with random sleep scheme. In the random sleep scheme, each agent independently and randomly decides whether to inquire the sub-gradient information of its local objective function at each iteration. The algorithm not only generalizes distributed algorithms with variable working nodes and multi-step consensus-based algorithms, but also extends some existing randomized convex set intersection results. We investigate the algorithm convergence properties under two types of stepsizes: the randomized diminishing stepsize that is heterogeneous and calculated by individual agent, and the fixed stepsize that is homogeneous. Then we prove that the estimates of the agents reach consensus almost surely and in mean, and the consensus point is the optimal solution with probability 1, both under randomized stepsize. Moreover, we analyze the algorithm error bound under fixed homogeneous stepsize, and also show how the errors depend on the fixed stepsize and update rates.

关键词： Distributed optimization sub-gradient algorithm random sleep multi-agent systems randomized algorithm

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Distributed Coordination Load Shedding of Islanded Microgrids Basedon sub-gradient algorithm

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IEEE ACCESS 2017年 5卷 27879-27886页

作者： Wu, Xi Feng, Shuang Jiang, Ping Southeast Univ Sch Elect Engn Nanjing 210096 Jiangsu Peoples R China Jiangsu Prov Key Lab Smart Grid Technol & Equipme Nanjing 210096 Jiangsu Peoples R China

This paper proposes a novel distributed coordination load shedding (DCLS) approach for an islanded microgrid (MG) using sub-gradient algorithm of multi-agent system. The main objective is to achieve practical and optimal LS and obtain an optimum amount of load to be shed in a fully distributed manner under large disturbances. To coordinate the controllable loads (CLs) in an MG, an LS level (LSL) is first defined and evaluated locally to take the CL capacity and the LS willingness into consideration. Then, by updating the LSLs and the local frequency deviation measured based on frequency-inertia dynamics response, the proposed DCLS can be accomplished based on the sub-gradient algorithm. More importantly, only local information is needed to be updated during the entire DCLS process. Hence, the power supply demand balance can be well maintained, the utilization of LS can be significantly improved, and the requirements for communication topology changes can be adaptively met in a fully distributed way. The simulation results indicate that the proposed sub-gradient-based distributed coordination algorithm and corresponding DCLS are effective and adaptive.

关键词： Distributed load shedding frequency dynamics response islanded microgrids multi-agent system sub-gradient algorithm

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Joint Optimization for Quality Selection and Resource Allocation of Live Video Streaming in Internet of Vehicles

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IEEE TRANSACTIONS ON SERVICES COMPUTING 2024年第4期17卷 1607-1621页

作者： Dai, Penglin Wu, Meiting Li, Ke Wu, Xiao Ding, Yan Southwest Jiaotong Univ Sch Comp & Artificial Intelligence Chengdu 611756 Peoples R China Minist Educ Engn Res Ctr Sustainable Urban Intelligent Transpo Chengdu 611756 Peoples R China SUNY Binghamton Dept Comp Sci Binghamton NY 13902 USA

Live Video Streaming (LVS) services are critical in supporting real-time applications in Internet of Vehicles (IoV) by transmitting real-time generated video content from streaming server to vehicles. Due to restricted spectrum resources and high vehicle mobility, LVS suffers from notable performance degradation. Moreover, existing strategies such as buffer size control and edge caching, are designed for video-on-demand service, which is ineffective for LVS in IoV. Accordingly, we investigate the problem of LVS-IoV by synthesizing multicasting and Scalable Video Coding-based encoding with the goal of maximizing Quality of Experience (QoE), which is defined as the weighted sum of video quality, rebuffering time, and quality variation. The LVS-IoV is decoupled into three sub-problems: vehicle grouping, quality selection, and resource allocation. First, we propose a K-means-based vehicle grouping method that considers geographical distribution, velocity, and dynamic channels. Second, we determine the quality selection of each group based on the Value Decomposition Network for maximizing overall video quality. This network utilizes global value function decomposition and centralized training to achieve fast convergence, followed by distributed execution. Lastly, we propose a sub-gradient algorithm to achieve optimal resource allocation. We build simulation model and perform extensive evaluation, which demonstrates its superiority compared to other competitive methods.

关键词： Internet of vehicles multi-agent reinforcement learning multicast-based live video streaming quality adaptation and resource allocation sub-gradient algorithm Internet of vehicles multi-agent reinforcement learning multicast-based live video streaming quality adaptation and resource allocation sub-gradient algorithm

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Power Allocation Schemes Based on Deep Learning for Distributed Antenna Systems

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IEEE ACCESS 2020年 8卷 31245-31253页

作者： Qian, Gongbin Li, Zhukun He, Chunlong Li, Xingquan Ding, Xue Shenzhen Univ Shenzhen Key Lab Adv Machine Learning & Applicat Shenzhen 518060 Guangdong Peoples R China

In recent years, a lot of power allocation algorithms have been proposed to maximize spectral efficiency (SE) and energy efficiency (EE) for the distributed antenna systems (DAS). However, the traditional iterative power allocation algorithms are difficult to be implemented in reality because of their high computational complexity. With the development of machine learning algorithms, it has been proved that the machine learning method has excellent learning ability and low computational complexity, which can approximate the traditional iterative power allocation well and be easily to be implemented in reality. In this paper, we propose a new deep neural network (DNN) model for DAS. From the perspective of machine learning, traditional iterative algorithms can be regarded as a nonlinear mapping between user channel realizations and optimal power allocation schemes. Therefore, we train the DNN to learn the nonlinear mapping between the user channel realizations and the corresponding power allocation schemes based on the traditional iterative algorithm. Then, a power allocation schemes based on DNN method is developed to maximize SE and EE for DAS. The simulation results show that the proposed scheme can not only obtain the almost similar performance as the traditional iterative algorithm, but also reduce much online computational time.

关键词： Distributed antenna systems deep learning power allocation algorithm sub-gradient algorithm spectral efficiency energy efficiency

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Distributed optimisation for resource allocation with event-triggered communication over general directed topology

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INTERNATIONAL JOURNAL OF SYSTEMS SCIENCE 2018年第6期49卷 1119-1130页

作者： Shi, Xiasheng Wang, Yuandong Song, Sumian Yan, Gangfeng Zhejiang Univ Coll Elect Engn Dept Syst Sci & Control Hangzhou 310000 Zhejiang Peoples R China

This paper focuses on the resource allocation problem(RAP) with constraints under a fixed general directed topology by using the distributed sub-gradient algorithm with event-triggered scheme in multi-agent systems, where each agent owns a cost function and its state value is bounded. The distributed sub-gradient algorithm aims to minimise the total cost by a distributed manner while achieving an optimal solution. Unlike centralised methods, the triggering condition and algorithm for each agent are fully decentralised. At each instant of time, each agent updates its state by employing the states which are collected from itself and its neighbouring agents at their last triggering time. In order to illustrate the effectiveness of the proposed sub-gradient algorithm with event-triggered control law, one simulation example is presented before the conclusion.

关键词： sub-gradient algorithm event-triggered resource allocation

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Using general triangle inequalities within quadratic convex reformulation method

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OPTIMIZATION METHODS & SOFTWARE 2023年第3期38卷 626-653页

作者： Lambert, Amelie Cnam CEDRIC 292 Rue St Martin FR-75141 Paris 03 France

We consider the exact solution of Problem (P) which consists in mini-mizing a quadratic function subject to quadratic constraints. We start with an explicit description of new general triangle inequalities that are derived from the ranges of the variables of (P). We show that they extend the triangle inequalities, introduced for the binary case, to variables that belong to a generic interval. We also prove that these inequalities cutfeasible solutions of McCormick envelopes, and we relate them to the literature. We then introduce (SDP), a strong semidefinite relaxation of (P), that we call "Shor's plus RLT plus Trian-gle', which includes both the McCormick envelopes and the general triangle inequalities. We further show how to compute a convex relaxation (P*) whose optimal value reaches the value of (SDP). In order to handle these inequalities in the solution of (SDP), we solve it by a heuristic that also serves as a separation algorithm. We then solve (P) to global optimality with a branch-and-bound based on (P*). Finally, we show that our method outperforms the compared solvers.

关键词： Quadratic convex relaxation valid inequalities global optimization semi-definite programming lagrangian duality sub-gradient algorithm quadratic programming

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Performance limits of stochastic sub-gradient learning, part II: Multi-agent case

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SIGNAL PROCESSING 2018年 144卷 253-264页

作者： Ying, Bicheng Sayed, Ali H. Univ Calif Los Angeles Dept Elect Engn Los Angeles CA 90024 USA Ecole Polytech Fed Lausanne Sch Engn Lausanne Switzerland

The analysis in Part I [1] revealed interesting properties for subgradient learning algorithms in the context of stochastic optimization. These algorithms are used when the risk functions are non-smooth or involve non-differentiable components. They have been long recognized as being slow converging methods. However, it was revealed in Part I [1] that the rate of convergence becomes linear for stochastic optimization problems, with the error iterate converging at an exponential rate alpha(i) to within an O(mu)-neighborhood of the optimizer, for some alpha is an element of (0, 1) and small step-size mu. The conclusion was established under weaker assumptions than the prior literature and, moreover, several important problems were shown to satisfy these weaker assumptions automatically. These results revealed that sub-gradient learning methods have more favorable behavior than originally thought. The results of Part I [1] were exclusive to single-agent adaptation. The purpose of current Part II is to examine the implications of these discoveries when a collection of networked agents employs subgradient learning as their cooperative mechanism. The analysis will show that, despite the coupled dynamics that arises in a networked scenario, the agents are still able to attain linear convergence in the stochastic case;they are also able to reach agreement within O(mu) of the optimizer. (C) 2017 Elsevier B.V. All rights reserved.

关键词： sub-gradient algorithm Affine-Lipschitz Linear rate Diffusion strategy Networked agents SVM LASSO

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Transmit power allocation of energy transmitters for throughput maximisation in wireless powered communication networks

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IET COMMUNICATIONS 2019年第9期13卷 1200-1206页

作者： Yu, Zhanwei Chi, Kaikai Zheng, Kechen Li, Yanjun Cheng, Zhen Zhejiang Univ Technol Sch Comp Sci & Technol Hangzhou 310023 Zhejiang Peoples R China

Radio-frequency (RF) energy harvesting is one promising technology to power the nodes in wireless networks. This study focuses on large-scale wireless powered communication networks having multiple RF energy transmitters (ETs) and sinks, which almost have not been investigated previously. The authors aim to optimise the throughput via optimizing the transmit power allocation of ETs subject to a total power budget. Specifically, for the sum-throughput maximisation (STM) problem, they firstly formulate it to be a non-linear optimisation problem, then prove its convexity and finally propose an efficient dual sub-gradient algorithm to solve it. Owing to the throughput unfairness among nodes of the STM approach, they further consider the common-throughput maximisation (CTM;i.e. the worst node's throughput) and propose a very efficient algorithm for it. This algorithm divides the CTM problem into a master problem and a subproblem. The subproblem of determining the feasibility of a given common-throughput is solved by transforming it to a linear problem whose optimal solution indicates the feasibility. The master problem of determining the maximal common-throughput is solved by using the bisection search method. Simulation results demonstrate the effectiveness of the CTM approach to mitigate the throughput unfairness problem at the cost of decreased sum-throughput.

关键词： radiofrequency power transmission radio networks telecommunication power management energy harvesting wireless sensor networks optimisation transmit power allocation energy transmitters wireless powered communication networks radio-frequency energy harvesting RF promising technologies wireless networks sinks ETs subject total power budget sum-throughput maximisation problem nonlinear optimisation problem sub-gradient algorithm common-throughput maximisation worst node CTM problem master problem linear problem whose optimal solution maximal common-throughput throughput unfairness problem decreased sum-throughput

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Variable selection and collinearity processing for multivariate data via row-elastic-net regularization

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ASTA-ADVANCES IN STATISTICAL ANALYSIS 2022年第1期106卷 79-96页

作者： Chen, Bingzhen Zhai, Wenjuan Kong, Lingchen Renmin Univ China Inst Stat & Big Data 59 Zhongguancun Ave Beijing 100872 Peoples R China Cangzhou Jiaotong Coll Dept Appl Math Cangzhou 061100 Peoples R China Beijing Jiaotong Univ Dept Appl Math Beijing 100044 Peoples R China

Multivariate data is collected in many fields, such as chemometrics, econometrics, financial engineering and genetics. In multivariate data, heteroscedasticity and collinearity occur frequently. And selecting material predictors is also a key issue when analyzing multivariate data. To accomplish these tasks, multivariate linear regression model is often constructed. We thus propose row-sparse elastic-net regularized multivariate Huber regression model in this paper. For this new model, we proof its grouping effect property and the property of resisting sample outliers. Based on the KKT condition, an accelerated proximal sub-gradient algorithm is designed to solve the proposed model and its convergency is also established. To demonstrate the accuracy and efficiency, simulation and real data experiments are carried out. The numerical results show that the new model can deal with heteroscedasticity and collinearity well.

关键词： Robust estimator Multivariate linear regression Collinearity Row-sparsity sub-gradient algorithm

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Optimal Bandwidth Allocation for Multi-Spot-Beam Satellite Communication Systems

Optimal Bandwidth Allocation for Multi-Spot-Beam Satellite C...

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International Conference on Mechatronic Sciences, Electric Engineering and Computer (MEC)

作者： Wang, Heng Liu, Aijun Pan, Xiaofei Jia, Luliang PLA Univ Sci & Technol Coll Commun Engn Nanjing Jiangsu Peoples R China

ISBN: (纸本)9781479925650

Due to the scarceness of the on-board bandwidth resource in multi-spot-beam satellite communication systems, it is important to enhance the bandwidth utilization efficiency. To this end, in this paper, we propose solving the problem of bandwidth allocation. We first formulated the problem of bandwidth allocation as a convex optimization, taking account into a trade-off between the maximum system total capacity and fairness among spot beams. Then we used sub-gradient algorithm to search the Lagrange multiplier and obtained the optimal bandwidth allocation for each spot beam. Simulation results show that compared with the uniform or proportional bandwidth allocation algorithm, the proposed optimal bandwidth allocation algorithm improves the fairness among spot beams.

关键词： Multi-spot-beam satellite communication system bandwidth allocation convex optimization sub-gradient algorithm

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