A Distributionally Robust Optimization Approach to the NASA Langley Uncertainty Quantification Challenge

TL;DR

This paper presents a novel methodology combining distributionally robust optimization and importance sampling to address the NASA Langley Uncertainty Quantification Challenge, providing both practical algorithms and theoretical guarantees.

Contribution

It introduces an integrated approach that leverages distributionally robust optimization with importance sampling, solved via sampled linear programs, and offers statistical guarantees.

Findings

Effective numerical performance demonstrated

Theoretical statistical guarantees established

Applicable to complex uncertainty quantification problems

Abstract

We study a methodology to tackle the NASA Langley Uncertainty Quantification Challenge problem, based on an integration of robust optimization, more specifically a recent line of research known as distributionally robust optimization, and importance sampling in Monte Carlo simulation. The main computation machinery in this integrated methodology boils down to solving sampled linear programs. We will illustrate both our numerical performances and theoretical statistical guarantees obtained via connections to nonparametric hypothesis testing.