Globalized distributionally robust optimization based on samples

TL;DR

This paper introduces globalized distributionally robust optimization models that balance robustness and conservatism by selecting a core set and sample space based on data, with reformulations into semi-definite programs and numerical analysis.

Contribution

It proposes novel GDRO models that incorporate a core set and sample space, providing a new way to control robustness and conservatism in DRO.

Findings

Reformulation of GDRO models into semi-definite programs

Numerical experiments illustrating the impact of sample space size

Demonstration of the relationship between objective values and core set size

Abstract

It is known that the set of perturbed data is key in robust optimization (RO) modelling. Distributionally robust optimization (DRO) is a methodology used for optimization problems affected by random parameters with uncertain probability distribution. In terms of the information of the perturbed data, it is essential to estimate an appropriate support set of the probability distribution in formulating DRO models. In this paper, we introduce two globalized distributionally robust optimization (GDRO) models which choose a core set based on data and a sample space containing the core set to balance the degree of robustness and conservatism at the same time. The degree of conservatism can be controlled by the expected distance of random parameters from the core set. Under some assumptions, we further reformulate several GDRO models into tractable semi-definite programs. In addition, numerical experiments are provided showing the relationship between the optimal objective values of the GDRO models and the size of the sample space and the core set.