Multivariate stochastic approximation using a simultaneous perturbation gradient approximation

Spall, James C.

doi:10.1109/9.119632

Cited by 1,845 publications

(1,418 citation statements)

References 24 publications

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“…We will not present the formal conditions for convergence and asymptotic normality of SPSA, as such conditions are available in many references (e.g., Dippon and Renz, 1997;Gerencsér, 1999;Spall, 1992. These conditions are essentially identical to the standard conditions for convergence of SA algorithms, with the exception of the additional conditions on the user-generated perturbation vector ∆ k .…”

Section: Copyright Springer Heidelberg 2004mentioning

confidence: 99%

“…Under reasonably general conditions (see Spall, 1992, or Spall, 2003, the SPSA and FDSA algorithms achieve the same level of statistical accuracy for a given number of iterations even though SPSA uses only 1|p times the number of function evaluations of FDSA (since each gradient approximation uses only 1|p the number of function evaluations).…”

Section: Copyright Springer Heidelberg 2004mentioning

confidence: 99%

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Stochastic Optimization

Spall

2011

Handbook of Computational Statistics

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Section: Copyright Springer Heidelberg 2004mentioning

confidence: 99%

Section: Copyright Springer Heidelberg 2004mentioning

confidence: 99%

Stochastic Optimization

Spall

2011

Handbook of Computational Statistics

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“…The proposed method (SASP) is obtained by hybridization of the two methods, the simulated annealing algorithm [4] and the descent method where the gradient [6] is estimate by using the simultaneous perturbation.…”

Section: The Sasp Methodsmentioning

confidence: 99%

The Mean-Variance-CVaR model for Portfolio Optimization Modeling using a Multi-Objective Approach Based on a Hybrid Method

Aboulaïch¹,

Ellaia²,

Moumen³

2010

Math. Model. Nat. Phenom.

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Abstract. In this paper we present a new hybrid method, called SASP method. We propose the hybridization of two methods, the simulated annealing (SA), which belong to the class of global optimization based on the principles of thermodynamics, and the descent method were we estimate the gradient using the simultaneous perturbation. This hybrid method gives better results. We use the Normal Boundary Intersection approach (NBI) based on the SASP method to solve a portfolio optimization problem. Such problem is a multi-objective optimization problem, in order to solve this problem we use three statistical quantities: the expected value, the variance and the Conditional Value-at-Risk (CVaR). The purpose of this work is to find the efficient boundary of the considered multi-objective problem using the NBI method based on the SASP method.

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“…FD requires 2N measurements, which is usually not very efficient. The SP method, as introduced by Spall (1987) and more fully analyzed in Spall (1992), overcomes this drawback. The essential feature of SP is its underlying gradient approximation that requires only two measurements per iteration independent of the dimension N .…”

Section: General Experiments Settingsmentioning

confidence: 99%

Gradient Estimation for Multicomponent Maintenance Systems with Age-Replacement Policy

Heidergott

Farenhorst-Yuan

2010

Operations Research

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We consider multicomponent maintenance systems with an F -failure group age-replacement policy: it keeps failed components idling until F components are failed and then replaces all failed components together with the nonfailed components whose age has passed the critical threshold age n for components of type n. With each maintenance action, costs are associated. We derive various unbiased gradient estimators based on the measure-valued differentiation approach for the gradient of the average cost. Each estimator has its own domain of applicability. We also compare the performance of our gradient estimators when applied to stochastic optimization with other general gradient-free methods.

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Multivariate stochastic approximation using a simultaneous perturbation gradient approximation

Cited by 1,845 publications

References 24 publications

Stochastic Optimization

Stochastic Optimization

The Mean-Variance-CVaR model for Portfolio Optimization Modeling using a Multi-Objective Approach Based on a Hybrid Method

Gradient Estimation for Multicomponent Maintenance Systems with Age-Replacement Policy

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