Distributed primal-dual optimisation method with uncoordinated time-varying step-sizes

This paper is concerned with the distributed optimisation problem over a multi-agent network, where the objective function is described by a sum of all the local objectives of agents. The target of agents is to collectively reach an optimal solution while minimising the global objective function. Under the assumption that the information exchange among agents is depicted by a sequence of time-varying undirected graphs, a distributed optimisation algorithm with uncoordinated time-varying step-sizes is presented, which signifies that the step-sizes of agents are not always uniform per iteration. In light of some reasonable assumptions, this paper fully conducts an explicit analysis for the convergence rate of the optimisation method. A striking feature is that the algorithm has a geometric convergence rate even if the step-sizes are time-varying and uncoordinated. Simulation results on two numerical experiments in power systems show effectiveness and performance of the proposed algorithm.     

Inexact dual averaging method for distributed multi-agent optimization

We consider a distributed convex optimization problem over a network where multiple agents collectively try to minimize a sum of local convex functions of the same variables, each of which is available to one specific agent only. For solving this optimization problem, we present an inexact version of the dual averaging method. This extends recent results of Duchi (2012), which cover the error-free case, to the case where an error is present in calculating the subgradient of the objective function or in computing the projection. We show that when the errors decrease at appropriate rates, our method achieves the same convergence rate as in the error-free case. In particular, the convergence of the method is also established for nonsummable errors. We also provide numerical results to validate the theoretic results.     

Finite‐Time Average Consensus Based Approach for Distributed Convex Optimization

In this paper, we consider a distributed convex optimization problem where the objective function is an average combination of individual objective function in multi‐agent systems. We propose a novel Newton Consensus method as a distributed algorithm to address the problem. This method utilises the efficient finite‐time average consensus method as an information fusion tool to construct the exact Newtonian global gradient direction. Under suitable assumptions, this strategy can be regarded as a distributed implementation of the classical standard Newton method and eventually has a quadratic convergence rate. The numerical simulation and comparison experiment show the superiority of the algorithm in convergence speed and performance.     

Finite time distributed distance‐constrained shape stabilization and flocking control for d‐dimensional undirected rigid formations

Most of the existing results on distributed distance‐constrained rigid formation control establish asymptotic or exponential convergence. To further improve the convergence rate, we explain in this paper how to modify existing gradient controllers to obtain finite time stability. For point agents modeled by single integrators, the controllers proposed in this paper drive the whole formation to locally converge to a desired shape with finite settling time. We also show for undirected triangular formation shape control, if all the agents start with non‐collinear positions, then the formation will converge to the desired shape in finite time. For agents modeled by double integrators, the proposed controllers allow all agents to both achieve the same velocity and reach a desired shape in finite time. All controllers are totally distributed. Simulations are also provided to validate the proposed control strategies. Copyright © 2015 John Wiley & Sons, Ltd.     

Constrained optimal consensus in multi-agent systems with single- and double-integrator dynamics

ABSTRACT

This paper fully studies distributed optimal consensus problem in undirected dynamical networks. We consider a group of networked agents that are supposed to rendezvous at the optimal point of a collective convex objective function. Each agent has no knowledge about the global objective function and only has access to its own local objective function, which is a portion of the global one, and states information of agents within its neighbourhood set. In this setup, all agents coordinate with their neighbours to seek the consensus point that minimises the network's global objective function. In the current paper, we consider agents with single-integrator and double-integrator dynamics. Further, it is supposed that agents' movements are limited by some convex inequality constraints. In order to find the optimal consensus point under the described scenario, we combine the interior-point optimisation algorithm with a consensus protocol and propose a distributed control law. The associated convergence analysis based on Lyapunov stability analysis is provided.     

Altruistic agents in uncertain dynamic games

The distributed operation of dynamic systems, such as traffic networks and the power grid, can be viewed as a dynamic game among their control agents. As the agents respond to one another’s decisions by resolving their problems, they trace a trajectory in decision space that, if convergent, arrives at a fixed point. Thus, two issues of concern are the convergence to attractors and their location relative to Pareto optimal solutions. This paper addresses these issues in games where each agent continually solves a problem from a family of unconstrained, but general optimization problems. Specifically, it delivers simple yet effective problem transformations to influence the convergence to and location of attractors—these transformations are referred to as altruistic factors and the agents that implement them are called altruistic agents. This paper proposes algorithms to draw attractors towards Pareto optimal solutions: for the case of quadratic functions, a thorough analysis of the rate of convergence is provided; for the case of general functions, a trust-region-based algorithm is proposed. An application of this game-theoretic framework is improvement of the quality of the solutions attained by distributed model predictive control, particularly in scenarios whose objective functions are quadratic and whose dynamics are linear. The text was submitted by the authors in English.     

Generalization of Linear Cyclic Pursuit With Application to Rendezvous of Multiple Autonomous Agents

Cyclic pursuit is a simple distributed control law in which agent i pursues agent i+1 modulo n. We generalize existing results and show that by selecting the gains of the agents, the point of convergence of these agents can be controlled. The condition for convergence, the range of controller gains and the reachable set where convergence can occur are studied. It is also shown that the sequence in which an agent pursues another does not affect the point of convergence     

Convergence speed in distributed consensus over dynamically switching random networks

Characterizing convergence speed is one of the most important research challenges in the design of distributed consensus algorithms for networked multi-agent systems. In this paper, we consider a group of agents that communicate via a dynamically switching random information network. Each link in the network, which represents the directed/undirected information flow between any ordered/unordered pair of agents, could be subject to failure with a certain probability. Hence we model the information flow using dynamically switching random graphs. We characterize the convergence speed for the distributed discrete-time consensus algorithm over a variety of random networks with arbitrary weights. In particular, we propose the asymptotic and per-step (mean square) convergence factors as measures of the convergence speed and derive the exact value for the per-step (mean square) convergence factor. Numerical examples are also given to illustrate our theoretical results.     

无线传感网中分布式信号检测的多维特征值算法优化研究

在大规模无线传感网的分布式信号检测中,针对相关性较高并有一定冗余度的数据集,在保证数据采集可信任的情况下,通过高效算法提高精度是重要的研究方向。 提出一种分散功率算法DPM,用于分布式计算样本协方差矩阵的最大特征值,通过将平均共识和迭代功率法相结合,在相对少量样本和有限次数迭代的条件下,实现了协方差矩阵最大特征值的较快收敛速度和较高精度估计。对比MECD算法和DST算法,仿真结果表明,新算法有效减少了信号样本数和迭代次数,收敛速度较快,可获得更高的检测精度。     

Gibbs sampling based distributed OFDMA resource allocation

In this article, we present a distributed resource and power allocation scheme for muRip]e-resource wireless cellular networks. The global optimization of multi-cell multi-link resource allocation problem is known to be NP-hard in the general case. We use Gibbs sampling based algorithms to perform a distributed optimization that would lead to the global optimum of the problem. The objective of this article is to show how to use the Gibbs sampling （GS） algorithm and its variant the Metropolis-Hastings （MH） algorithm. We also propose an enhanced method of the MH algorithm, based on a priori known target state distribution, which improves the convergence speed without increasing the complexity. Also, we study different temperature cooling strategies and investigate their impact on the network optimization and convergence speed. Simulation results have also shown the effectiveness of the proposed methods.     

Communication constraints in the average consensus problem

The interrelationship between control and communication theory is becoming of fundamental importance in many distributed control systems, such as the coordination of a team of autonomous agents. In such a problem, communication constraints impose limits on the achievable control performance. We consider as instance of coordination the consensus problem. The aim of the paper is to characterize the relationship between the amount of information exchanged by the agents and the rate of convergence to the consensus. We show that time-invariant communication networks with circulant symmetries yield slow convergence if the amount of information exchanged by the agents does not scale well with their number. On the other hand, we show that randomly time-varying communication networks allow very fast convergence rates. We also show that by adding logarithmic quantized data links to time-invariant networks with symmetries, control performance significantly improves with little growth of the required communication effort.     

一种基于4Bit编码的深度学习梯度压缩算法

对梯度数据进行压缩,是一种减少多机间通信开销的有效方法,如MXNet系统中的2Bit方法等。但这类方法存在一个突出的问题,即过高的压缩比会导致精度及收敛速度下降,尤其是对规模较大的深度神经网络模型。针对上述问题,提出了一种新的4Bit梯度压缩策略。该方法采用4个比特位表示一个具体的梯度值(通常为32位的浮点数)。相对于2Bit,该方法能够对梯度值进行更细粒度的近似,从而提高训练结果的准确率和收敛性。进一步地,根据网络模型每一层梯度特性的不同,选择不同的近似阈值,使得压缩后的数值更合理,从而进一步加快模型的收敛速度并提高最终准确率;具体地,兼顾操作的方便性和分布的合理性,根据每层梯度特性的不同,设置3组不同的阈值,以满足不同层梯度差异化特性的需求。实验结果表明,使用多组阈值的4Bit梯度压缩策略虽然在加速方面略逊于2Bit方法,但其准确率更高,实用性更强,能够在保持模型更高精度的前提下减少分布式深度学习系统的通信开销,这对于在资源受限环境下实现性能更好的深度学习模型非常有意义。     

梯度收缩法在局部放电定位中的应用

使用梯度收缩法开展了变压器局部放电源的超声定位工作。梯度收缩法结合了牛顿法和共轭梯度法的优点,应用目标函数的二阶导数,收敛速度快,具有牛顿法的“二次收敛”特性,并具有较高的精确度。实验结果表明,梯度收缩法能有效解决变压器局部放电点定位问题。     

Memory gradient method with Goldstein line search

In this paper, we present a multi-step memory gradient method with Goldstein line search for unconstrained optimization problems and prove its global convergence under some mild conditions. We also prove the linear convergence rate of the new method when the objective function is uniformly convex. Numerical results show that the new algorithm is suitable to solve large-scale optimization problems and is more stable than other similar methods in practical computation.     

基于值分布的多智能体分布式深度强化学习算法

近年来深度强化学习在一系列顺序决策问题中取得了巨大的成功,使其为复杂高维的多智能体系统提供有效优化的决策策略成为可能.然而在复杂的多智能体场景中,现有的多智能体深度强化学习算法不仅收敛速度慢,而且算法的稳定性无法保证.本文提出了基于值分布的多智能体分布式深度确定性策略梯度算法(multi-agent distribut...     

An iterative scheme for distributed model predictive control using Fenchel's duality

We present an iterative distributed version of Han's parallel method for convex optimization that can be used for distributed model predictive control (DMPC) of industrial processes described by dynamically coupled linear systems. The underlying decomposition technique relies on Fenchel's duality and allows subproblems to be solved using local communications only. We investigate two techniques aimed at improving the convergence rate of the iterative approach and illustrate the results using a numerical example. We conclude by discussing open issues of the proposed method and by providing an outlook on research in the field.     

蚁群算法在移动Agent迁移中的应用研究

移动Agent提供了一种全新的分布计算范型.移动Agent技术给分布式系统的设计、实现和维护都带来了新的活力.旅行Agent问题是一类复杂的组合优化问题,目的在于解决移动Agent在不同主机间移动时如何根据移动Agent的任务和其他约束条件来规划最优的迁移路线.蚁群算法作为一种新的生物进化算法,具有并行、正反馈和启发式搜索等特点,是一种解决旅行Agent问题的有效手段,受到了广泛的关注,但它与其他进化算法一样存在易陷入局部最小的缺点.在蚁群算法的基础上,通过修改它的信息素轨迹更新规则,引入自适应的信息素挥发系数来提高收敛速度和算法的全局最优解搜索能力,从而使得移动Agent在移动时以最优的效率和最短的时间来完成迁移.仿真结果表明,改进的算法在解的性能和收敛速度上均优于相关算法.     

Coverage control by multi-robot networks with limited-range anisotropic sensory

This article considers the deployment of a network of robotic agents with limited-range communication and anisotropic sensing capabilities. We encode the environment coverage provided by the network by means of an expected-value objective function. This function has a gradient which is not amenable to distributed computation. We provide a constant-factor approximation of this measure via an alternative aggregate objective function, whose gradient is spatially distributed over the limited-range Delaunay proximity graph. We characterise the smoothness properties of the aggregate expected-value function and propose a distributed deployment algorithm that enables the network to optimise it. Simulations illustrate the results.     

Distributed Optimization for Model Predictive Control of Linear-Dynamic Networks

A linear-dynamic network consists of a directed graph in which the nodes represent subsystems and the arcs model dynamic couplings. The local state of each subsystem evolves according to discrete linear dynamics that depend on the local state, local control signals, and control signals of upstream subsystems. Such networks appear in the model predictive control (MPC) of geographically distributed systems such as urban traffic networks and electric power grids. In this correspondence, we propose a decomposition of the quadratic MPC problem into a set of local subproblems that are solved iteratively by a network of agents. A distributed algorithm based on the method of feasible directions is developed for the agents to iterate toward a solution of the subproblems. The local iterations require relatively low effort to arrive at a solution but at the expense of high communication among neighboring agents and with a slower convergence rate.