Importance sampling in stochastic programming: A Markov chain Monte Carlo approach
File(s)
Accepted version
Author(s)
Parpas, P
Ustun, B
Webster, MD
Tran, QK
Type
Journal Article
Abstract
Stochastic programming models are large-scale optimization problems that are used to facilitate decision making under uncertainty. Optimization algorithms for such problems need to evaluate the expected future costs of current decisions, often referred to as the recourse function. In practice, this calculation is computationally difficult as it requires the evaluation of a multidimensional integral whose integrand is an optimization problem. In turn, the recourse function has to be estimated using techniques such as scenario trees or Monte Carlo methods, both of which require numerous functional evaluations to produce accurate results for large-scale problems with multiple periods and high-dimensional uncertainty. In this work, we introduce an importance sampling framework for stochastic programming that can produce accurate estimates of the recourse function using a small number of samples. Our framework combines Markov chain Monte Carlo methods with kernel density estimation algorithms to build a nonparametric importance sampling distribution, which can then be used to produce a lower-variance estimate of the recourse function. We demonstrate the increased accuracy and efficiency of our approach using variants of well-known multistage stochastic programming problems. Our numerical results show that our framework produces more accurate estimates of the optimal value of stochastic programming models, especially for problems with moderate variance, multimodal, or rare-event distributions.
Date Issued
2015-04-24
Date Acceptance
2014-09-01
Citation
Informs Journal on Computing, 2015, 27 (2), pp.358-377
ISSN
1526-5528
Publisher
INFORMS (Institute for Operations Research and Management Sciences)
Start Page
358
End Page
377
Journal / Book Title
Informs Journal on Computing
Volume
27
Issue
2
Copyright Statement
© 2015, INFORMS