Distributionally Robust Optimization Under Moment Uncertainty with Application to Data-Driven Problems

• 成果类型: Article
• 署名作者: Delage, Erick; Ye, Yinyu
• 署名单位: Universite de Montreal; HEC Montreal; Stanford University
• 刊物名称: OPERATIONS RESEARCH
• ISSN/ISSBN: 0030-364X
• DOI: 10.1287/opre.1090.0741
• 发表日期: 2010
• 页码: 595-612
• 关键词: convex-programs; sample roots

摘要

Stochastic programming can effectively describe many decision-making problems in uncertain environments. Unfortunately, such programs are often computationally demanding to solve. In addition, their solution can be misleading when there is ambiguity in the choice of a distribution for the random parameters. In this paper, we propose a model that describes uncertainty in both the distribution form (discrete, Gaussian, exponential, etc.) and moments (mean and covariance matrix). We demonstrate that for a wide range of cost functions the associated distributionally robust (or min-max) stochastic program can be solved efficiently. Furthermore, by deriving a new confidence region for the mean and the covariance matrix of a random vector, we provide probabilistic arguments for using our model in problems that rely heavily on historical data. These arguments are confirmed in a practical example of portfolio selection, where our framework leads to better-performing policies on the true distribution underlying the daily returns of financial assets.