多智能体系统的多步近似次梯度随机投影优化算法

基于切换网络下带有随机时延和随机通讯噪声的多智能体系统模型,提出分布式多步近似次梯度随机投影算法,并对算法的收敛性进行分析.首先,利用网络扩维的方法将含随机时延的通讯网络转化为无时延网络;其次,提出近似次梯度概念,并设计多步近似次梯度随机批量投影算法,批量随机投影可以避免在实际问题中整体约束集合不易获得而导致投影算子不...     

Stochastic sub-gradient algorithm for distributedoptimization with random sleep scheme

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.     

Implementation of a subgradient projection algorithm

This paper discusses the implementation of an algorithm due to Sreedharan [8] for the minimization, subject to linear constraints, of an objective function composed of the sum of a piecewise-affine, convex function with a smooth, strictly convex function. Successful techniques for two subproblems arising in the algorithm, a projection problem and a line search problem, are described in detail. Computational experience with the algorithm on several test problems is presented.     

Implementation of a subgradient projection algorithm II

This paper discusses the implementation of a subgradient projection algorithm due to Sreedharan [13] for the minimization, subject to a finite number of smooth, convex constraints, of an objective function which is the sum of a smooth, strictly convex function and a piecewise smooth convex function. Computational experience with the algorithm on several test problems and comparison of this experience with previously published results is presented.     

多个体切换网络分布式量化次梯度优化算法

由于已有的分布式次梯度算法大多基于理想的假设：网络拓扑是有向平衡的,构成网络的个体间通信的是各个个体某个状态变量的完全精确的信息。针对更一般的非平衡切换网络以及实际生活中网络通道的带宽限制,提出一种基于有限量化信息通信的切换网络分布式量化次梯度优化算法。在非平衡切换网络中,通过设计具有有限量化水平的一致量化器使所有信息在发送之前都经过量化,利用非二次李雅普诺夫函数方法,证明了所提出的多个体分布式量化次梯度优化算法的收敛性。最后仿真实例验证了所提算法的有效性,而且通过调节量化水平参数,在相同的带宽条件下,可提高信息传输速率,使网络中的个体更快地达到一致。该方法弱化了对刻画网络拓扑的邻接矩阵的假设及对网络带宽的要求,更具实用性。     

Saddle points of discrete Markov zero-sum game with stopping

We study the sufficient conditions for the existence of a saddle point of a time-dependent discrete Markov zero-sum game up to a given stopping time. The stopping time is allowed to take either a finite or an infinite non-negative random variable with its associated objective function being well-defined. The result enables us to show the existence of the saddle points of discrete games constructed by Markov chain approximation of a class of stochastic differential games.     

次梯度投影算子求解图像重建问题的并行策略

将次梯度投影迭代算法应用到数字图像重建问题。将图像重建问题转化为求一个加权最小二乘问题,导出次梯度投影算子在该问题下的具体迭代形式,并采用并行计算策略重建算法。通过三维数值实验对比次梯度投影迭代算法与常用的SART算法,验证算法的可行性和效率。     

带事件触发机制的分布式量化随机无梯度投影算法

本文研究多智能体系统的分布式约束优化问题,系统中的每个智能体仅知道自身的局部目标函数和全局非空约束集,通过与邻居节点进行信息交互,最终协同求出优化问题的最优解.本文所提出的算法针对通信网络为时变不平衡有向图,且每个智能体不知道它的出度的情况.同时考虑到现实中通信带宽有限和通讯成本的限制,应用基于编译码方案的量化技术对节...     

基于随机投影的K-means算法研究

对于大量的高维训练数据,数据降维是提高存储和计算效率、避免维数灾难的有效手段。提出了一种方法:首先基于随机投影理论对原始数据集进行随机投影变换,将数据集矩阵A映射为ā,而后再对矩阵ā执行K-means聚类算法,这样不仅能降低数据集的维度,同时也能减少执行K-means算法的时间,并且能够保证良好的聚类效果。最后在人工数据集和面部图像数据集上的仿真实验验证了该理论的有效性和准确性。     

离散非线性零和博弈的事件驱动最优控制方案

在求解离散非线性零和博弈问题时,为了在有效降低网络通讯和控制器执行次数的同时保证良好的控制效果,本文提出了一种基于事件驱动机制的最优控制方案.首先,设计了一个采用新型事件驱动阈值的事件驱动条件,并根据贝尔曼最优性原理获得了最优控制对的表达式.为了求解该表达式中的最优值函数,提出了一种单网络值迭代算法.利用一个神经网络构建评价网.设计了新的评价网权值更新规则.通过在评价网、控制策略及扰动策略之间不断迭代,最终获得零和博弈问题的最优值函数和最优控制对.然后,利用Lyapunov稳定性理论证明了闭环系统的稳定性.最后,将该事件驱动最优控制方案应用到了两个仿真例子中,验证了所提方法的有效性.     

基于随机投影技术的矩阵填充算法的改进

利用随机投影加速技术将高维矩阵的奇异值分解(SVD)投影到一个低维子空间上进行,可以减少SVD消耗的时间。定义了奇异值随机投影压缩算子,取代之前的奇异值压缩算子,并用这个算子改进了定点连续(FPC)算法得到FPCrp算法。对改进前后的算法进行了大量实验,结果表明:随机投影技术能够在保持算法鲁棒性和精度的同时,节省50%以上的时间。因此,基于随机投影技术的矩阵填充算法更适合求解大规模问题。     

The singular zero-sum differential game with stability usingH ∞ control theory

In this paper we consider the zero-sum, infinite-horizon, linear quadratic differential game. We derive sufficient conditions for the existence of (almost) equilibria as well as necessary conditions. Contrary to all classical references we allow for singular weighting on the minimizing player in the cost criterion. It turns out that this problem has a strong relation with the singularH _∞ problem with state feedback, i.e., theH _∞ problem where the direct feedthrough matrix from control input to output is not necessarily injective.     

Adaptive dynamic programming for online solution of a zero-sum differential game

This paper will present an approximate/adaptive dynamic programming(ADP) algorithm,that uses the idea of integral reinforcement learning(IRL),to determine online the Nash equilibrium solution for the two-player zerosum differential game with linear dynamics and infinite horizon quadratic cost.The algorithm is built around an iterative method that has been developed in the control engineering community for solving the continuous-time game algebraic Riccati equation(CT-GARE),which underlies the game problem.We here show how the ADP techniques will enhance the capabilities of the offline method allowing an online solution without the requirement of complete knowledge of the system dynamics.The feasibility of the ADP scheme is demonstrated in simulation for a power system control application.The adaptation goal is the best control policy that will face in an optimal manner the highest load disturbance.     

基于随机投影与集成学习的离群点检测算法

针对传统基于相似度的离群点检测算法在高维不均衡数据集上效果不够理想的问题,提出一种新颖的基于随机投影与集成学习的离群点检测（ensemble learning and random projection-based outlier detection,EROD）框架。算法首先集成多个随机投影方法对高维数据进行降维,提升数据多样性;然后集成多个不同的传统离群点检测器构建异质集成模型,增加算法鲁棒性;最后使用异质模型对降维后的数据进行训练,训练后的模型经过两次优化组合以降低泛化误差,输出最终的对象离群值,离群值高的对象被算法判定为离群点。分别在四个不同领域的高维不均衡真实数据集上进行对比实验,结果表明该算法与传统离群点检测算法和基于集成学习的离群点检测算法相比,在AUC和precision@n值上平均提高了3.6%和14.45%,证明EROD算法具有处理高维不均衡数据异常的优势。     

An effective subgradient algorithm for the generalized assignment problem

A modified subgradient algorithm is presented for the generalized assignment problem, which, like the classical assignment problem, is concerned with the minimum cost assignment of agents to jobs. The generalized assignment problem, however, permits differences in job performance efficiencies among agents and thereby allows the possibility that each agent may be assigned more than a single job, as long as each job is ultimately assigned and the total resources available to every agent are not exceeded. A two stage heuristic algorithm using a modified subgradient approach and branch and bound is developed for solving the problem. By computing step sizes precisely and using the dual as a bound, the algorithm is shown to be particularly effective and easy to program and implement. A numerical example is presented to illustrate the model and method, and computational experience is cited for problems containing up to 12,000 0–1 variables.     

利用模糊次梯度算法求解拉格朗日松弛对偶问题

针对利用次梯度算法处理拉格朗日松弛对偶问题时，计算过程容易出现振荡，求解效率较低的问题，首先提出了一种基于模糊理论的次梯度算法，利用隶属度函数给出迭代过程中所有次梯度的合适权重，并将它们线性加权得到新的迭代方向；其次证明了算法的收敛性；最后通过仿真实验验证了该方法的有效性．     

Distributed cooperative control algorithm for optimal power sharing for AC microgrids using Cournot game theory

Neural Computing and Applications - Research on the optimal power allocation of large-scale distributed generator (DG) units based on user power generation to access microgrids (MGs) in a...     

基于随机支付的合作博弈分析

在确定性支付的合作博弈中,Ｓｈａｐｌｅｙ值以其优良的特性在合作博弈分配解中占据着非常重要的作用,但现实生活中更多情形下的支付是不确定的,参与人要在这种情形下作出选择．因此,基于Ｓｈａｐｌｅｙ值的表述公式,构建基于随机支付的合作博弈模型,构造边际值和转换值两个合作解,并举例说明随机支付情形下两个解不再相等．最后,给出了两个解相等的一个博弈子类．     

非线性零和微分对策的事件触发自适应动态规划算法

针对一类非线性零和微分对策问题,本文提出了一种事件触发自适应动态规划(event-triggered adaptive dynamic programming,ET--ADP)算法在线求解其鞍点.首先,提出一个新的自适应事件触发条件.然后,利用一个输入为采样数据的神经网络(评价网络)近似最优值函数,并设计了新型的神经网络权值更新律使得值函数、控制策略及扰动策略仅在事件触发时刻同步更新.进一步地,利用Lyapunov稳定性理论证明了所提出的算法能够在线获得非线性零和微分对策的鞍点且不会引起Zeno行为.所提出的ET--ADP算法仅在事件触发条件满足时才更新值函数、控制策略和扰动策略,因而可有效减少计算量和降低网络负荷.最后,两个仿真例子验证了所提出的ET--ADP算法的有效性.     

Eigen-distribution on random assignments for game trees

In this Letter, we investigate a special distribution, called eigen-distribution, on random assignments for a class of game trees . There are two cases, where the assignments to leaves are independently distributed (ID) and correlated distributed (CD). In the ID case, we prove that the distributional probability ? belongs to , and ? is a strictly increasing function on rounds k∈[1,∞). In the CD case, we propose a reverse assigning technique (RAT) to form two particular sets of assignments, 1-set and 0-set, then show that the E¹-distribution (namely, a particular distribution on the assignments of 1-set such that all the deterministic algorithms have the same complexity) is the unique eigen-distribution for in the global distribution.