Journal article
Distributionally Robust Optimization with Confidence Bands for Probability Density Functions
INFORMS journal on optimization, Vol.4(1), pp.65-89
01/2022
DOI: 10.1287/ijoo.2021.0059
Abstract
Distributionally robust optimization (DRO) has been introduced for solving stochastic programs in which the distribution of the random variables is unknown and must be estimated by samples from that distribution. A key element of DRO is the construction of the ambiguity set, which is a set of distributions that contains the true distribution with a high probability. Assuming that the true distribution has a probability density function, we propose a class of ambiguity sets based on confidence bands of the true density function. As examples, we consider the shape-restricted confidence bands and the confidence bands constructed with a kernel density estimation technique. The former allows us to incorporate the prior knowledge of the shape of the underlying density function (e.g., unimodality and monotonicity), and the latter enables us to handle multidimensional cases. Furthermore, we establish the convergence of the optimal value of DRO to that of the underlying stochastic program as the sample size increases. The DRO with our ambiguity set involves functional decision variables and infinitely many constraints. To address this challenge, we apply duality theory to reformulate the DRO to a finite-dimensional stochastic program, which is amenable to a stochastic subgradient scheme as a solution method.
Details
- Title: Subtitle
- Distributionally Robust Optimization with Confidence Bands for Probability Density Functions
- Creators
- Xi Chen - New York UniversityQihang Lin - University of IowaGuanglin Xu - University of North Carolina at Charlotte
- Resource Type
- Journal article
- Publication Details
- INFORMS journal on optimization, Vol.4(1), pp.65-89
- DOI
- 10.1287/ijoo.2021.0059
- ISSN
- 2575-1484
- eISSN
- 2575-1492
- Language
- English
- Date published
- 01/2022
- Academic Unit
- Business Analytics
- Record Identifier
- 9984380598302771
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