Exploiting structure in distributionally robust optimization

Abstract

Decision-making under uncertainty is a fundamental challenge across many areas, such as engineering, finance, and healthcare. While stochastic optimization provides a principled framework by modeling uncertainty through probability distributions, identifying the correct distribution is not always straightforward; hence, a deeper layer of "uncertain" uncertainty emerges. This thesis addresses this challenge through distributionally robust optimization (DRO), which hedges decisions against an ambiguity set of plausible distributions consistent with observed data. The central contribution is the exploitation of structural prior knowledge, specifically the independence of uncertainty components , to construct tighter ambiguity sets. This reduces conservativeness while preserving rigorous statistical guarantees. Three interconnected contributions are developed in this work: (i) structured ambiguity sets tailored to independent uncertainty components; (ii) tractable reformulations and complexity-reduction procedures for the associated DRO problems; and (iii) a distributionally robust model predictive control scheme for linear systems under unknown disturbance distributions, in which the computational burden of DRO is handled entirely offline, yielding a practically implementable controller. The proposed framework enables reliable, high-performance data-driven decisions in settings where the true probability distribution is unknown but partial structural information about the independence of the uncertainty components is available.