Displaying similar documents to “Efficiency of the Stochastic Approximation Method”

Asymptotic normality of randomly truncated stochastic algorithms

Jérôme Lelong (2013)

ESAIM: Probability and Statistics

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We study the convergence rate of randomly truncated stochastic algorithms, which consist in the truncation of the standard Robbins–Monro procedure on an increasing sequence of compact sets. Such a truncation is often required in practice to ensure convergence when standard algorithms fail because the expected-value function grows too fast. In this work, we give a self contained proof of a central limit theorem for this algorithm under local assumptions on the expected-value function,...

On the Recursive Estimation of the Location and of the Size of the Mode of a Probability Density

Djeddour, Khédidja, Mokkadem, Abdelkader, Pelletier, Mariane (2008)

Serdica Mathematical Journal

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2000 Mathematics Subject Classification: 62G07, 62L20. Tsybakov [31] introduced the method of stochastic approximation to construct a recursive estimator of the location q of the mode of a probability density. The aim of this paper is to provide a companion algorithm to Tsybakov's algorithm, which allows to simultaneously recursively approximate the size m of the mode. We provide a precise study of the joint weak convergence rate of both estimators. Moreover, we introduce...

On the convergence of moments in the almost sure central limit theorem for stochastic approximation algorithms

Peggy Cénac (2013)

ESAIM: Probability and Statistics

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We study the almost sure asymptotic behaviour of stochastic approximation algorithms for the search of zero of a real function. The quadratic strong law of large numbers is extended to the powers greater than one. In other words, the convergence of moments in the almost sure central limit theorem (ASCLT) is established. As a by-product of this convergence, one gets another proof of ASCLT for stochastic approximation algorithms. The convergence result is applied to several examples as...

Global stochastic approximation

Ryszard Zieliński

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CONTENTS1. Intuitive background. Statement of the problem...................................................................... 52. General structure of global stochastic approximation processes............................................... 73. The fundamental theorem on convergence in distribution............................................................ 104. Absolute continuity of the limit distribution 4.1. Introductory remarks................................................................................................................

A Global Stochastic Optimization Method for Large Scale Problems

W. El Alem, A. El Hami, R. Ellaia (2010)

Mathematical Modelling of Natural Phenomena

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In this paper, a new hybrid simulated annealing algorithm for constrained global optimization is proposed. We have developed a stochastic algorithm called ASAPSPSA that uses Adaptive Simulated Annealing algorithm (ASA). ASA is a series of modifications to the basic simulated annealing algorithm (SA) that gives the region containing the global solution of an objective function. In addition, Simultaneous Perturbation Stochastic Approximation...

Some stochastic comparison results for series and parallel systems with heterogeneous Pareto type components

Lakshmi Kanta Patra, Suchandan Kayal, Phalguni Nanda (2018)

Applications of Mathematics

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We focus on stochastic comparisons of lifetimes of series and parallel systems consisting of independent and heterogeneous new Pareto type components. Sufficient conditions involving majorization type partial orders are provided to obtain stochastic comparisons in terms of various magnitude and dispersive orderings which include usual stochastic order, hazard rate order, dispersive order and right spread order. The usual stochastic order of lifetimes of series systems with possibly different...