Assessing the Role of Distributional Robust Optimization in Statistical Decision-Making Under Uncertainty

Posted: Feb 05, 2020

• Grace Brooks
• Hailey Butler
• Hannah Turner

Abstract

Statistical decision-making under uncertainty represents one of the most fundamental challenges across numerous domains, from finance and healthcare to engineering and public policy. Traditional approaches to decision-making under uncertainty have predominantly relied on stochastic optimization frameworks that assume precise knowledge of probability distributions governing uncertain parameters. However, this assumption frequently proves untenable in practice, where decision-makers must contend with distributional ambiguity, limited data, and potential model misspecification. The consequences of such limitations can be severe, leading to decisions that perform poorly when the true distribution deviates from assumed models. Distributional robust optimization has emerged as a promising paradigm for addressing these challenges by explicitly accounting for uncertainty in the underlying probability distributions. Rather than optimizing for a single nominal distribution, DRO seeks decisions that perform well across a family of possible distributions, known as an ambiguity set. This approach acknowledges the inherent limitations in our knowledge of true distributions while providing formal guarantees on performance under distributional uncertainty. Our research makes several distinctive contributions to this field. First, we develop a novel hybrid DRO framework that integrates Wasserstein distance-based ambiguity sets with adaptive regularization techniques, creating a more nuanced approach to managing distributional uncertainty. Second, we introduce a methodology for dynamically adjusting ambiguity set sizes based on available data quality and quantity, addressing a critical limitation of static ambiguity sets. Third, we provide extensive empirical validation across multiple domains, demonstrating that our approach achieves superior performance compared to existing methods while maintaining computational feasibility.