Global Stochastic Optimization with Low-Dispersion Point Sets

Yakowitz, S.; L’Ecuyer, Pierre; Vázquez-Abad, Felisa J.

doi:10.1287/opre.48.6.939.12393

Cited by 59 publications

(36 citation statements)

References 24 publications

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“…that satisfy the large deviations principle (cf. e.g., [16], [32]). Assumption L2 can be viewed as a simple extension of L1.…”

Section: Where φ(· ·) Satisfies the Conditions In L1mentioning

confidence: 99%

“…A detailed review of various gradient estimation techniques can be found in [20] and [11]. Also of relevance to our work is the low-dispersion point sets method of [32], which uses the idea of quasirandom search for continuous global optimization and large deviation principle to choose the evaluation points within the decision domain and to (adaptively) determine the number of simulation observations to be allocated to these points.…”

Section: Introductionmentioning

confidence: 99%

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A Model Reference Adaptive Search Method for Stochastic Global Optimization

Hu¹,

Fu²,

Marcus³

2008

Communications in Information and Systems

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We propose a randomized search method called Stochastic Model Reference Adaptive Search (SMRAS) for solving stochastic optimization problems in situations where the objective functions cannot be evaluated exactly, but can be estimated with some noise (or uncertainty), e.g., via simulation. The method generalizes the recently proposed Model Reference Adaptive Search (MRAS) method for deterministic optimization, and is based on sampling from an underlying probability distribution "model" on the solution space, which is updated iteratively after evaluating the performance of the samples at each iteration. We prove global convergence of SMRAS in a general stochastic setting, and carry out numerical studies to illustrate its performance. An emphasis of this paper is on the application of SMRAS for solving static stochastic optimization problems with either continuous or discrete domains; its various applications for solving dynamic decision making problems can be found in [6].

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“…that satisfy the large deviations principle (cf. e.g., [16], [32]). Assumption L2 can be viewed as a simple extension of L1.…”

Section: Where φ(· ·) Satisfies the Conditions In L1mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

A Model Reference Adaptive Search Method for Stochastic Global Optimization

Hu¹,

Fu²,

Marcus³

2008

Communications in Information and Systems

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“…In particular, Yakowitz and Lugosi [35] developed a method that at certain iterations samples new solutions from a fixed global distribution and ensures that every sampled point has "enough" observations, and at other times it adaptively resamples previously sampled points. Yakowitz et al [34] proposed two approaches that use low-dispersion point sets and emphasize how the number of such points should be determined depending on the problem and the simulation budget. Baumert and Smith [5] proposed an approach based on pure random search that estimates the objective function value at each solution θ by averaging all observations within a certain distance from θ and discussed how this distance should decrease in order for the method to converge in probability.…”

Section: Introductionmentioning

confidence: 99%

Adaptive random search for continuous simulation optimization

Andradóttir

Prudius

2010

Naval Research Logistics

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Abstract:We present, analyze, and compare three random search methods for solving stochastic optimization problems with uncountable feasible regions. Our adaptive search with resampling (ASR) approach is a framework for designing provably convergent algorithms that are adaptive and may consequently involve local search. The deterministic and stochastic shrinking ball (DSB and SSB) approaches are also convergent, but they are based on pure random search with the only difference being the estimator of the optimal solution [the DSB method was originally proposed and analyzed by Baumert and Smith]. The three methods use different techniques to reduce the effects of noise in the estimated objective function values. Our ASR method achieves this goal through resampling of already sampled points, whereas the DSB and SSB approaches address it by averaging observations in balls that shrink with time. We present conditions under which the three methods are convergent, both in probability and almost surely, and provide a limited computational study aimed at comparing the methods. Although further investigation is needed, our numerical results suggest that the ASR approach is promising, especially for difficult problems where the probability of identifying good solutions using pure random search is small. © 2010 Wiley Periodicals, Inc. Naval Research Logistics 57: 583-604, 2010 Keywords: continuous stochastic optimization; local search; pure random search; global convergence in probability and almost surely; adaptive search with resampling; deterministic and stochastic shrinking ball methods

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“…7]), the implementation has been far less successful: no adaptive method appears to have been proposed that is practically implementable in a wide range of general multivariate problems (e.g., " the optimal choice [of gain sequence] involves the Hessian of the risk [loss] function, which is typically unknown and hard to estimate," from Yakowitz et al [44]). Let us summarize some of the existing approaches to illustrate the difficulties.…”

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confidence: 99%

Adaptive stochastic approximation by the simultaneous perturbation method

Spall

Proceedings of the 37th IEEE Conference on Decision and Control (Cat. No.98CH36171)

112

246

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Abstract-Stochastic approximation (SA) has long been applied for problems of minimizing loss functions or root finding with noisy input information. As with all stochastic search algorithms, there are adjustable algorithm coefficients that must be specified, and that can have a profound effect on algorithm performance. It is known that choosing these coefficients according to an SA analog of the deterministic Newton-Raphson algorithm provides an optimal or near-optimal form of the algorithm. However, directly determining the required Hessian matrix (or Jacobian matrix for root finding) to achieve this algorithm form has often been difficult or impossible in practice. This paper presents a general adaptive SA algorithm that is based on a simple method for estimating the Hessian matrix, while concurrently estimating the primary parameters of interest. The approach applies in both the gradient-free optimization (Kiefer-Wolfowitz) and root-finding/stochastic gradient-based (Robbins-Monro) settings, and is based on the "simultaneous perturbation (SP)" idea introduced previously. The algorithm requires only a small number of loss function or gradient measurements per iteration-independent of the problem dimension-to adaptively estimate the Hessian and parameters of primary interest. Aside from introducing the adaptive SP approach, this paper presents practical implementation guidance, asymptotic theory, and a nontrivial numerical evaluation. Also included is a discussion and numerical analysis comparing the adaptive SP approach with the iterate-averaging approach to accelerated SA.

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Global Stochastic Optimization with Low-Dispersion Point Sets

Cited by 59 publications

References 24 publications

A Model Reference Adaptive Search Method for Stochastic Global Optimization

A Model Reference Adaptive Search Method for Stochastic Global Optimization

Adaptive random search for continuous simulation optimization

Adaptive stochastic approximation by the simultaneous perturbation method

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