Comparison of the efficiency of deterministic and stochasticalgorithms for visual reconstruction

Piecewise continuous reconstruction of real-valued data can be formulated in terms of nonconvex optimization problems. Both stochastic and deterministic algorithms have been devised to solve them. The simplest such reconstruction process is the weak string. Exact solutions can be obtained for it and are used to determine the success or failure of the algorithms under precisely controlled conditions. It is concluded that the deterministic algorithm (graduated nonconvexity) outstrips stochastic (simulated annealing) algorithms both in computational efficiency and in problem-solving power     

随机优化算法的基本数学原理与实践

试图探究随机优化算法的有效性,即收敛性存在背后的原理,据原理构造出两个随机优化算法。随机优化算法是对生物的一种模拟,用于解决函数或者策略的寻优问题。证明了随机优化算法要取得全局收敛所需的条件,并通过仿真验证了提出的两个随机优化算法的有效性。     

Compensatability and optimal compensation of systems with white parameters in the delta domain

Using the delta operator, the strengthened discrete-time optimal projection equations for optimal reduced-order compensation of systems with white stochastic parameters are formulated in the delta domain. The delta domain unifies discrete time and continuous time. Moreover, when formulated in this domain, the efficiency and numerical conditioning of algorithms improves when the sampling rate is high. Exploiting the unification, important theoretical results, algorithms and compensatability tests concerning finite and infinite horizon optimal compensation of systems with white stochastic parameters are carried over from discrete time to continuous time. Among others, we consider the finite-horizon time-varying compensation problem for systems with white stochastic parameters and the property mean-square compensatability (ms-compensatability) that determines whether a system with white stochastic parameters can be stabilised by means of a compensator. In continuous time, both of these appear to be new. This also holds for the associated numerical algorithms and tests to verify ms-compensatability. They are illustrated with three numerical examples that reveal several interesting theoretical and numerical issues. A fourth example illustrates the improvement of both the efficiency and numerical conditioning of the algorithms. This is of vital practical importance for digital control system design when the sampling rate is high.     

Weighted averaging and stochastic approximation

We explore the relationship between weighted averaging and stochastic approximation algorithms, and study their convergence via a sample-path analysis. We prove that the convergence of a stochastic approximation algorithm is equivalent to the convergence of the weighted average of the associated noise sequence. We also present necessary and sufficient noise conditions for convergence of the average of the output of a stochastic approximation algorithm in the linear case. We show that the averaged stochastic approximation algorithms can tolerate a larger class of noise sequences than the stand-alone stochastic approximation algorithms.This research was supported by the National Science Foundation through Grants ECS-9410313 and ECS-9501652.This research was supported by the National Science Foundation through NYI Grant IRI-9457645.     

Stochastic approximation methods for identification and control--A survey

Stochastic search techniques have been the essential part for most identification and self-organizing or learning control algorithms for stochastic systems. Stochastic approximation search algorithms have been very popular among the researchers in these areas because of their simplicity of implementation, convergence properties, as well as intuitive appeal to the investigator. This paper presents an exposition of the stochastic approximation algorithms and their application to various parameter identification and self-organizing control algorithms.     

ElasticSim: A Toolkit for Simulating Workflows with Cloud Resource Runtime Auto-Scaling and Stochastic Task Execution Times

Resource provisioning and scheduling are crucial for cloud workflow applications. Simulation is one of the most promising evaluation methods for different resource provisioning and scheduling algorithms. However, existing simulators for Cloud workflow applications fail to provide support for resource runtime auto-scaling and stochastic task execution time modeling. In this paper, a workflow simulator ElasticSim is introduced, which is an extension of the popular used CloudSim simulator by adding support for resource runtime auto-scaling and stochastic task execution time modeling. Most of existing workflow scheduling algorithms are static and are based on deterministic task execution times. By the aid of ElasticSim, the practical performance of existing static algorithms, when they are put into practice with stochastic task execution times, is evaluated. Experimental results show that about 2.8 % to 20 % additional resource rental cost is incurred for different cases and workflow deadlines are violated for most cases because of stochastic task execution times. Therefore, ElasticSim is a promising platform for evaluating the practical performance of workflow resource provisioning and scheduling algorithms, which supports resource runtime auto-scaling and stochastic task execution time modeling.     

混沌优化方法及其应用*

利用混沌运动的遍历性、随机性、“规律性”等特点，本文提出了一种混沌优化方法（ＣＯＡ）。用混沌优化方法对一类连续复杂对象的优化问题进行优化，其效率比一些目前广泛应用的随机优化方法如ＳＡＡ，ＣＡ等要高得多，而且使用方便。     

考虑本地作业流时的网格资源调度算法

研究了网格资源上有和没有本地作业流两种情况下两种网格资源调度算法的性能优劣对比情况。建立了一个资源的本地随机作业流模型,提出了最快处理器可用资源优先(HRARF)和最适合作业并行度可用资源优先(MSNARF)两种网格资源调度算法,并对所提出的两种算法在资源有和没有本地作业流两种情况下调度网格作业的完工时间进行仿真。仿真结果显示,在资源负载较重时,在有和没有本地作业流两种情况下,HRARF和MSNARF两种算法的性能优劣对比正好相反。在网格中,两种算法在资源共享时和资源独占时的性能优劣对比可能不同。     

随机性优化算法有效性定量对比评价方法

针对随机性优化算法寻优结果不可重复的特点,为该类优化算法提供了一种定量对比评价算法有效性的方法。该方法针对单个或一组测试函数的多次优化结果进行统计分析,得到一个能够在概率意义上定量表征不同随机性算法求解单个或一组测试函数的有效性优劣关系的因子。利用该方法,对采用同步或异步全局最优粒子信息更新模式的两种标准粒子群优化算法（PSO）版本进行有效性对比评价,给出了同步和异步模式PSO算法求解无约束单目标连续变量优化问题的有效性优劣关系。     

Convergence of concurrent Markov chain Monte-Carlo algorithms

We examine the parallel execution of a class of stochastic algorithms called Markov chain Monte-Carlo (MCMC) algorithms. We focus on MCMC algorithms in the context of image processing, using Markov random field models. Our parallelisation approach is based on several, concurrently running, instances of the same stochastic algorithm that deal with the whole data set. Firstly we show that the speed-up of the parallel algorithm is limited because of the statistical properties of the MCMC algorithm. We examine coupled MCMC as a remedy for this problem. Secondly, we exploit the parallel execution to monitor the convergence of the stochastic algorithms in a statistically reliable manner. This new convergence measure for MCMC algorithms performs well, and is an improvement on known convergence measures. We also link our findings with recent work in the statistical theory of MCMC.     

Proper Generalized Decompositions and Separated Representations for the Numerical Solution of High Dimensional Stochastic Problems

Uncertainty quantification and propagation in physical systems appear as a critical path for the improvement of the prediction of their response. Galerkin-type spectral stochastic methods provide a general framework for the numerical simulation of physical models driven by stochastic partial differential equations. The response is searched in a tensor product space, which is the product of deterministic and stochastic approximation spaces. The computation of the approximate solution requires the solution of a very high dimensional problem, whose calculation costs are generally prohibitive. Recently, a model reduction technique, named Generalized Spectral Decomposition method, has been proposed in order to reduce these costs. This method belongs to the family of Proper Generalized Decomposition methods. It takes part of the tensor product structure of the solution function space and allows the a priori construction of a quasi optimal separated representation of the solution, which has quite the same convergence properties as a posteriori Hilbert Karhunen-Loève decompositions. The associated algorithms only require the solution of a few deterministic problems and a few stochastic problems on deterministic reduced basis (algebraic stochastic equations), these problems being uncoupled. However, this method does not circumvent the “curse of dimensionality” which is associated with the dramatic increase in the dimension of stochastic approximation spaces, when dealing with high stochastic dimension. In this paper, we propose a marriage between the Generalized Spectral Decomposition algorithms and a separated representation methodology, which exploits the tensor product structure of stochastic functions spaces. An efficient algorithm is proposed for the a priori construction of separated representations of square integrable vector-valued functions defined on a high-dimensional probability space, which are the solutions of systems of stochastic algebraic equations.     

A deterministic analysis of stochastic approximation withrandomized directions

We study the convergence of two stochastic approximation algorithms with randomized directions: the simultaneous perturbation stochastic approximation algorithm and the random direction Kiefer-Wolfowitz algorithm. We establish deterministic necessary and sufficient conditions on the random directions and noise sequences for both algorithms, and these conditions demonstrate the effect of the “random” directions on the “sample-path” behavior of the algorithms studied. We discuss ideas for further research in the analysis and design of these algorithms     

Convergence Analysis of Weighted Stochastic Gradient Identification Algorithms Based on Latest‐Estimation for ARX Models

In this paper, weighted stochastic gradient (WSG) algorithms for ARX models are proposed by modifying the standard stochastic gradient identification algorithms. In the proposed algorithms, the correction term is a weighting combination of the correction terms of the standard stochastic gradient (SG) algorithm in the current and last recursive steps. In addition, a latest estimation based WSG (LE‐WSG) algorithm is also established. The convergence performance of the proposed LE‐WSG algorithm is then analyzed. It is shown by a numerical example that both the WSG and LE‐WSG algorithms can possess faster convergence speed and higher convergence precision compared with the standard SG algorithms if the weighting factor is appropriately chosen.     

Efficiency of the random search method

The efficiency of random search algorithms for both deterministic and stochastic optimization problems is considered.     

Modified stochastic gradient parameter estimation algorithms for a nonlinear two-variable difference system

This paper proposes a stochastic gradient algorithm and two modified stochastic gradient algorithms for a nonlinear two-variable difference system. The output and the input of a two-variable parameter system depend on time and on spatial coordinates. A stochastic gradient algorithm is introduced to estimate the unknown parameters. In order to increase the convergence rate but not to increase the computational effort, two modified stochastic gradient algorithms are also proposed. The simulation results indicate that the proposed methods are effective.     

Feedback estimation systems and the separation principle of stochastic control

Estimation systems with a feedback link have a structure similar to that encountered in the study of stochastic feedback control systems. A feedback estimation algorithm of a specific form is derived in this paper. This algorithm is shown to be superior to one based upon the separation principle of stochastic control and inferior to one employing a different feedback signal structure. The observed differences in performance of these algorithms give insight into a basic limitation on control policies derived from formal application of the separation principle.     

基于扩展的随机DAG的EST估算与任务调度

针对DAG调度算法中采取多次执行后的平均值估算任务的EST值问题,通过对DAG调度中常用的调度算法ETF算法进行分析提出基于扩展的随机DAG的调度方法SETF,给出扩展的随机DAG中节点的EST计算方法,以标准方差和平均值之和的数学期望表示,并以ETF算法为例进行实验模拟。实验结果表明,SETF算法相对于ETF算法,减少并行任务执行时间,并能更精确地预测任务调度的平均执行时间。     

String Methods for Stochastic Image and Shape Matching

Matching of images and analysis of shape differences is traditionally pursued by energy minimization of paths of deformations acting to match the shape objects. In the large deformation diffeomorphic metric mapping (LDDMM) framework, iterative gradient descents on the matching functional lead to matching algorithms informally known as Beg algorithms. When stochasticity is introduced to model stochastic variability of shapes and to provide more realistic models of observed shape data, the corresponding matching problem can be solved with a stochastic Beg algorithm, similar to the finite-temperature string method used in rare event sampling. In this paper, we apply a stochastic model compatible with the geometry of the LDDMM framework to obtain a stochastic model of images and we derive the stochastic version of the Beg algorithm which we compare with the string method and an expectation-maximization optimization of posterior likelihoods. The algorithm and its use for statistical inference is tested on stochastic LDDMM landmarks and images.     

General results on the convergence of stochastic algorithms

A deterministic approach is proposed for proving the convergence of stochastic algorithms of the most general form under necessary conditions on the input noise and reasonable conditions on the (nonnecessarily continuous) mean field. Emphasis is placed on the case where more than one stationary point exists. We also use this approach to prove the convergence of a stochastic algorithm with Markovian dynamics     

Robust real-time identification of linear systems with correlated noise

The problem of recursive robust identification of linear discrete-time single-input single-output dynamic systems with correlated disturbances is considered. Problems related to the construction of optimal robust stochastic approximation algorithms in the min-max sense are demonstrated. Since the optimal solution cannot be achieved in practice, several robustified stochastic approximation algorithms are derived on the basis of a suitable non-linear transformation of normalized residuals, as well as step-by-step optimization with respect to the weighting matrix of the algorithm. The convergence of the developed algorithms is established theoretically using the ordinary differential equation approach. Monte Carlo simulation results are presented for the quantitative performance evaluation of the proposed algorithms. The results indicate the most suitable algorithms for applications in engineering practice.