Parametric Scenario Optimization under Limited Data: A Distributionally Robust Optimization View
Year: 2019
Type: preprint
Abstract: We consider optimization problems with uncertain constraints that need to be satisfied probabilistically. When data are available, a common method to obtain feasible solutions for such problems is to impose sampled constraints, following the so-called scenario optimization approach. However, when the data size is small, the sampled constraints may not statistically support a feasibility guarantee on the obtained solution. This paper studies how to leverage parametric information and the power of Monte Carlo simulation to obtain feasible solutions for small-data situations. Our approach makes use of a distributionally robust optimization (DRO) formulation that translates the data size requirement into a Monte Carlo sample size requirement drawn from what we call a generating distribution. We show that, while the optimal choice of this generating distribution is the one eliciting the data or the baseline distribution in a nonparametric divergence-based DRO, it is not necessarily so in the parametric case. Correspondingly, we develop procedures to obtain generating distributions that improve upon these basic choices. We support our findings with several numerical examples.
Source: arXiv (Cornell University)
Authors: Lam, Henry, Li, Fengpei
Language: English
Field: Decision Sciences
Domain: Social Sciences
Open Access status: green
Awards: S&AS:FND:COLLAB:Unsupervised Rare Event Learning - With Applications on Autonomous Vehicles, G3387330441, CAREER: Optimization-based Quantification of Statistical Uncertainty in Stochastic and Simulation Analysis, A Sensitivity Approach to Assessing Model Uncertainty for Stochastic Systems, CAREER: Optimization-based Quantification of Statistical Uncertainty in Stochastic and Simulation Analysis, G6671297155
OpenAlex ID: W2941973645