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Asymptotic almost sure efficiency of averaged stochastic algorithms

SIAM JOURNAL ON CONTROL AND OPTIMIZATION 2000年第1期39卷 49-72页

作者： Pelletier, M Univ Versailles Math Lab F-78035 Versailles France

First, we de ne the notion of almost sure efficiency for a decreasing stepsize stochastic algorithm, and then we show that the averaging method, which gives asymptotically efficient algorithms, also gives asymptotically almost surely efficient algorithms. Moreover, we prove that the averaged algorithm also satis es a law of the iterated logarithm, a well as an almost sure central limit theorem.

关键词： stochastic algorithms central limit theorem almost sure invariance principles

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Characterizing Energy Landscapes of Peptides Using a Combination of stochastic algorithms

IEEE TRANSACTIONS ON NANOBIOSCIENCE

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IEEE TRANSACTIONS ON NANOBIOSCIENCE 2015年第5期14卷 545-552页

作者： Devaurs, Didier Molloy, Kevin Vaisset, Marc Shehu, Amarda Simeon, Thierry Cortes, Juan CNRS LAAS F-31400 Toulouse France Univ Toulouse LAAS F-31400 Toulouse France Rice Univ Dept Comp Sci Houston TX 77005 USA George Mason Univ Dept Comp Sci Fairfax VA 22030 USA

Obtaining accurate representations of energy landscapes of biomolecules such as proteins and peptides is central to the study of their physicochemical properties and biological functions. Peptides are particularly interesting, as they exploit structural flexibility to modulate their biological function. Despite their small size, peptide modeling remains challenging due to the complexity of the energy landscape of such highly-flexible dynamic systems. Currently, only stochastic sampling-based methods can efficiently explore the conformational space of a peptide. In this paper, we suggest to combine two such methods to obtain a full characterization of energy landscapes of small yet flexible peptides. First, we propose a simplified version of the classical Basin Hopping algorithm to reveal low-energy regions in the landscape, and thus to identify the corresponding meta-stable structural states of a peptide. Then, we present several variants of a robotics-inspired algorithm, the Transition-based Rapidly-exploring Random Tree, to quickly determine transition path ensembles, as well as transition probabilities between meta-stable states. We demonstrate this combined approach on met-enkephalin.

关键词： Energy landscape peptides stochastic algorithms

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ACCELERATED stochastic algorithms FOR NONCONVEX FINITE-SUM AND MULTIBLOCK OPTIMIZATION

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SIAM JOURNAL ON OPTIMIZATION 2019年第4期29卷 2753-2784页

作者： Lan, Guanghui Yang, Yu Georgia Inst Technol H Milton Stewart Sch Ind & Syst Engn Atlanta GA 30332 USA

In this paper, we present new stochastic methods for solving two important classes of nonconvex optimization problems. We first introduce a randomized accelerated proximal gradient (RapGrad) method for solving a class of nonconvex optimization problems whose objective function consists of the summation of m components and show that it can significantly reduce the number of gradient computations especially when the condition number L/mu (i.e., the ratio between the Lipschitz constant and negative curvature) is large. More specifically, RapGrad can save up to O(root m) gradient computations more than existing batch nonconvex accelerated gradient methods. Moreover, the number of gradient computations required by RapGrad can be O(m(1/6)L(1/2)/mu(1/2)) (at least O(m(2/3))) times smaller than the best-known randomized nonconvex gradient methods when L/mu >= m. Inspired by RapGrad, we also develop a new randomized accelerated proximal dual (RapDual) method for solving a class of multiblock nonconvex optimization problems coupled with linear constraints and some special structural properties. We demonstrate that RapDual can also save up to a factor of O(root m) block updates more than its batch counterpart, where m denotes the number of blocks. To the best of our knowledge, all these complexity results associated with RapGrad and RapDual seem to be new in the literature. We also illustrate potential advantages of these algorithms through our preliminary numerical experiments.

关键词： nonconvex optimization stochastic algorithms acceleration finite-sum optimization multiblock optimization

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COMPARISON OF THE EFFICIENCY OF DETERMINISTIC AND stochastic algorithms FOR VISUAL RECONSTRUCTION

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IEEE TRANSACTIONS ON PATTERN ANALYSIS AND MACHINE INTELLIGENCE 1989年第1期11卷 2-12页

作者： BLAKE, A Dept. of Comput. Sci. Edinburgh Univ. UK

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.

关键词： stochastic processes Simulated annealing Computational modeling Problem-solving Noise reduction Image motion analysis Computer science Glands Testing Biomembranes INSPEC: Controlled Indexing optimisation computer vision computerised picture processing INSPEC: Non-Controlled Indexing problem-solving power deterministic algorithms stochastic algorithms visual reconstruction nonconvex optimization weak string computational efficiency

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Benchmarking stochastic algorithms for Global Optimization Problems by Visualizing Confidence Intervals

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IEEE TRANSACTIONS ON CYBERNETICS 2017年第9期47卷 2924-2937页

作者： Liu, Qunfeng Chen, Wei-Neng Deng, Jeremiah D. Gu, Tianlong Zhang, Huaxiang Yu, Zhengtao Zhang, Jun Dongguan Univ Technol Sch Comp Sci & Network Secur Dongguan 523808 Peoples R China South China Univ Technol Sch Comp Sci & Engn Guangzhou 510006 Guangdong Peoples R China Univ Otago Dept Informat Sci Dunedin 9054 New Zealand Guilin Univ Elect Technol Sch Comp Sci & Engn Guilin 541004 Peoples R China Shandong Normal Univ Sch Informat Sci & Engn Jinan 250014 Shandong Peoples R China Kunming Univ Sci & Technol Sch Informat Engn & Automat Kunming 650500 Yunnan Peoples R China

The popular performance profiles and data profiles for benchmarking deterministic optimization algorithms are extended to benchmark stochastic algorithms for global optimization problems. A general confidence interval is employed to replace the significance test, which is popular in traditional benchmarking methods but suffering more and more criticisms. Through computing confidence bounds of the general confidence interval and visualizing them with performance profiles and (or) data profiles, our benchmarking method can be used to compare stochastic optimization algorithms by graphs. Compared with traditional benchmarking methods, our method is synthetic statistically and therefore is suitable for large sets of benchmark problems. Compared with some sample-mean-based benchmarking methods, e.g., the method adopted in black-boxoptimization-benchmarking workshop/competition, our method considers not only sample means but also sample variances. The most important property of our method is that it is a distribution-free method, i.e., it does not depend on any distribution assumption of the population. This makes it a promising benchmarking method for stochastic optimization algorithms. Some examples are provided to illustrate how to use our method to compare stochastic optimization algorithms.

关键词： Benchmarking computational budget evolutionary algorithms global optimization performance comparison stochastic algorithms

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Estimation of Systemic Shortfall Risk Measure Using stochastic algorithms

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SIAM JOURNAL ON FINANCIAL MATHEMATICS 2024年第3期15卷 700-733页

作者： Kaakai, Sarah Matoussi, Anis Tamtalini, Achraf Le Mans Univ Inst Risque & Assurance Lab Manceau Math Le Mans France Le Mans Univ Inst Risque & Assurance FR CNRS 2962 Le Mans France Ecole Polytech Ctr Math Appl CNRS Palaiseau France

Systemic risk measures were introduced to capture the global risk and the corresponding contagion effects that are generated by an interconnected system of financial institutions. To this purpose, two approaches were suggested. In the first one, systemic risk measures can be interpreted as the minimal amount of cash needed to secure a system after aggregating individual risks. In the second approach, systemic risk measures can be interpreted as the minimal amount of cash that secures a system by allocating capital to each single institution before aggregating individual risks. Although the theory behind these risk measures has been well investigated by several authors, the numerical part has been neglected so far. In this paper, we use stochastic algorithms schemes in estimating multivariate shortfall risk measure and prove that the resulting estimators are consistent and asymptotically normal. We also test numerically the performance of these algorithms on several examples.

关键词： multivariate risk measures shortfall risk stochastic algorithms stochastic root finding risk allocations

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A robust nonlinear inversion for the interpretation of magnetic anomalies caused by faults, thin dikes and spheres like structure using stochastic algorithms

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PURE AND APPLIED GEOPHYSICS 2007年第10期164卷 2023-2042页

作者： Asfahani, J. Tlas, M. State Atom Energy Commiss Dept Geol Damascus Syria State Atom Energy Commiss Div Math Damascus Syria

A geophysical interpretative method is proposed to depth, amplitude coefficient (effective magnetization intensity), and index parameter (effective magnetization inclination) determination of a buried structure from magnetic field data anomaly due to a fault, a thin dike or a sphere-like structure. The method is based on the nonlinearly constrained mathematical modelling and also on the stochastic optimization approaches. The proposed interpretative method was first tested on a theoretical synthetic model with different random errors, where a very close agreement was obtained between the assumed and the evaluated parameters. The validity of this method was also tested on practical field data taken from United States, Australia, India and Brazil, where available magnetic data existed and were previously analyzed by different interpretative methods. The agreement between the results obtained by our developed method and those obtained by the other geophysical methods is good.

关键词： magnetic anomaly mathematical modelling exponential penalty function stochastic algorithms

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stochastic algorithms for the estimation of an optimal solution of a LP problem. Convergence and central limit theorem

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COMMUNICATIONS IN STATISTICS-THEORY AND METHODS 2008年第20期37卷 3308-3318页

作者： Prieto-Rumeau, Tomas Univ Nacl Educ Distancia Dept Estadist Fac Ciencias E-28040 Madrid Spain

In this article, we consider a Linear Programming (LP) problem with unknown objective function. We introduce a class of stochastic algorithms to estimate an optimal solution of the LP problem. The almost sure convergence and the speed of convergence of these algorithms are analyzed. We also prove a central limit theorem for the estimation errors of the algorithms.

关键词： central limit theorem stochastic algorithms stochastic approximation

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Advancing Sustainable Energy: Analyzing stochastic algorithms and Q-Learning for Wind Farm Layout Optimization 5

Advancing Sustainable Energy: Analyzing Stochastic Algorithm...

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5th International Conference on Artificial Intelligence, Robotics and Control (AIRC)

作者： Elsheikh, Mohamed Yonis, Amr Magdy, Jessica Shehata, Omar M. German Univ Cairo Comp Sci Dept Fac Media Engn & Technol Cairo Egypt German Univ Cairo Mechatron Engn Dept Fac Engn & Mat Sci Cairo Egypt Multirobot Syst MRS Res Grp Cairo Egypt

ISBN: (纸本)9798350385083;9798350385076

This paper presents a comprehensive study on the optimization of wind farm layouts, a critical aspect of enhancing the efficiency and effectiveness of wind energy production. We delve into various optimization techniques, including Simulated Annealing, Genetic Algorithm, Particle Swarm Optimization, Moth Flame Optimization, and Deep Q-Learning. Each optimization technique is explored through a series of case studies, where different configurations and parameters are applied to assess their effectiveness in optimizing wind farm layouts. These techniques are evaluated based on criteria such as computational complexity, optimality of solutions, and repeatability of results. The paper's findings offer insightful comparisons and analyses of each technique, providing an understanding of their respective strengths and limitations in the context of wind farm layout optimization.

关键词： Sustainable Energy Wind Farm Layout Optimization Meta-Heuristic stochastic algorithms Multi-Cooperative Systems Simulated Annealing Genetic Algorithm Particle Swarm Moth Flame Reinforcement Learning Q-Learning

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Bootstrap Performance Profiles in stochastic algorithms Assessment

Bootstrap Performance Profiles in Stochastic Algorithms Asse...

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International Conference on Numerical Analysis and Applied Mathematics (ICNAAM)

作者： Costa, Lino Espirito Santo, Isabel A. C. P. Oliveira, Pedro Univ Minho Dept Prod & Syst Engn P-4710057 Braga Portugal Univ Porto Inst Ciencias Biomed Abel Salazar P-4099002 Oporto Portugal

ISBN: (纸本)9780735412873

Optimization with stochastic algorithms has become a relevant research field. Due to its stochastic nature, its assessment is not straightforward and involves integrating accuracy and precision. Performance profiles for the mean do not show the trade-off between accuracy and precision, and parametric stochastic profiles require strong distributional assumptions and are limited to the mean performance for a large number of runs. In this work, bootstrap performance profiles are used to compare stochastic algorithms for different statistics. This technique allows the estimation of the sampling distribution of almost any statistic even with small samples. Multiple comparison profiles are presented for more than two algorithms. The advantages and drawbacks of each assessment methodology are discussed.

关键词： performance profiles stochastic algorithms numerical optimization

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