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Enhancing Estimation and Uncertainty Quantification in Stochastic Optimization: Importance Sampling and Bootstrap Resampling /

Record Type:	Electronic resources : Monograph/item
Title/Author:	Enhancing Estimation and Uncertainty Quantification in Stochastic Optimization: Importance Sampling and Bootstrap Resampling /Xiaotie Chen.
Author:	Chen, Xiaotie,
Description:	1 electronic resource (108 pages)
Notes:	Source: Dissertations Abstracts International, Volume: 86-02, Section: B.
Notes:	Advisors: Woodruff, David L. Committee members: Loera, Jesus De; Strohmer, Thomas.
Contained By:	Dissertations Abstracts International86-02B.
Subject:	Applied mathematics.
Online resource:	http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=31328967
ISBN:	9798383608289

Enhancing Estimation and Uncertainty Quantification in Stochastic Optimization: Importance Sampling and Bootstrap Resampling /
Chen, Xiaotie,

Enhancing Estimation and Uncertainty Quantification in Stochastic Optimization: Importance Sampling and Bootstrap Resampling /Xiaotie Chen. - 1 electronic resource (108 pages)

Source: Dissertations Abstracts International, Volume: 86-02, Section: B.

This dissertation explores the applications of Monte Carlo and Bootstrap methods in stochastic optimization, focusing on enhancing computational efficiency and accuracy in solution evaluation and uncertainty quantification. For the purpose of computing the expected value of a stochastic optimization problem via simulation, we propose a method to efficiently construct importance sampling distributions using surrogate modeling. This method significantly reduces the need for repeated evaluations of the objective function, which are typically computationally intensive due to the reliance on optimization algorithms. Our method outperforms traditional Monte Carlo estimation and achieves significant speed-ups with good parallel efficiency. Additionally, we explore Monte Carlo sampling algorithms that utilize known distributions to construct confidence intervals around the optimality gap in two-stage and multi-stage stochastic programs. In scenarios where the distribution of uncertainty remains unknown, we discuss bootstrap and bagging algorithms that rely solely on sampled data to provide both a consistent sample-average solution and accurate confidence interval estimates. These methods are enhanced by integrating distribution estimation into resampling techniques to improve the precision of estimations under uncertainty. We also offer open-source software implementations of these algorithms. Extensive empirical studies show the effectiveness of the smoothed bootstrap and bagging methods, particularly for constructing confidence intervals with small data sets.

English

ISBN: 9798383608289Subjects--Topical Terms:

377601
Applied mathematics.
Subjects--Index Terms:

Monte Carlo sampling algorithms

Enhancing Estimation and Uncertainty Quantification in Stochastic Optimization: Importance Sampling and Bootstrap Resampling /
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520 $a This dissertation explores the applications of Monte Carlo and Bootstrap methods in stochastic optimization, focusing on enhancing computational efficiency and accuracy in solution evaluation and uncertainty quantification. For the purpose of computing the expected value of a stochastic optimization problem via simulation, we propose a method to efficiently construct importance sampling distributions using surrogate modeling. This method significantly reduces the need for repeated evaluations of the objective function, which are typically computationally intensive due to the reliance on optimization algorithms. Our method outperforms traditional Monte Carlo estimation and achieves significant speed-ups with good parallel efficiency. Additionally, we explore Monte Carlo sampling algorithms that utilize known distributions to construct confidence intervals around the optimality gap in two-stage and multi-stage stochastic programs. In scenarios where the distribution of uncertainty remains unknown, we discuss bootstrap and bagging algorithms that rely solely on sampled data to provide both a consistent sample-average solution and accurate confidence interval estimates. These methods are enhanced by integrating distribution estimation into resampling techniques to improve the precision of estimations under uncertainty. We also offer open-source software implementations of these algorithms. Extensive empirical studies show the effectiveness of the smoothed bootstrap and bagging methods, particularly for constructing confidence intervals with small data sets.
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