Higher-Order Expansion and Bartlett Correctability of Distributionally Robust Optimization

• 成果类型: Article; Early Access
• 署名作者: He, Shengyi; Lam, Henry
• 署名单位: Columbia University
• 刊物名称: MATHEMATICS OF OPERATIONS RESEARCH
• ISSN/ISSBN: 0364-765X
• DOI: 10.1287/moor.2023.0191
• 发表日期: 2025
• 关键词: likelihood confidence-intervals; Empirical Likelihood; Portfolio optimization; sensitivity-analysis; bootstrap; RISK; uncertainty; bounds; functionals; dependency

摘要

Distributionally robust optimization (DRO) is a worst-case framework for stochastic optimization under uncertainty that has drawn fast-growing studies in recent years. When the underlying probability distribution is unknown and observed from data, DRO suggests computing the worst-case distribution within a so-called uncertainty set that captures the involved statistical uncertainty. In particular, DRO with uncertainty set constructed as a statistical divergence neighborhood ball has been shown to provide a tool for constructing valid confidence intervals for nonparametric functionals and bears a duality with the empirical likelihood (EL). In this paper, we show how adjusting the ball size of such type of DRO can reduce higher-order coverage errors similar to the so-called Bartlett correction. Our correction, which applies to general von Mises differentiable functionals, is more general than the existing EL literature that only focuses on smooth function models or M-estimation. Moreover, we demonstrate a higher-order self-normalizing property of DRO regardless of the choice of divergence. Our approach builds on the development of a higher-order expansion of DRO, which is obtained through an asymptotic analysis on a fixed-point equation arising from the Karush-Kuhn-Tucker conditions.