Technical Note-A Data-Driven Approach to Beating SAA Out of Sample

• 成果类型: Article
• 署名作者: Gotoh, Jun-ya; Kim, Michael Jong; Lim, Andrew E. B.
• 署名单位: Chuo University; University of British Columbia; National University of Singapore; National University of Singapore
• 刊物名称: OPERATIONS RESEARCH
• ISSN/ISSBN: 0030-364X
• DOI: 10.1287/opre.2021.0393
• 发表日期: 2025
• 关键词: distributionally optimistic optimization; distributionally robust optimization; sample average approximation; Data-Driven Optimization; model uncertainty; worst case sensitivity; out-of-sample performance

摘要

Whereas solutions of distributionally robust optimization (DRO) problems can sometimes have a higher out-of-sample expected reward than the sample average approximation (SAA), there is no guarantee. In this paper, we introduce a class of distributionally optimistic optimization (DOO) models and show that it is always possible to beat SAA out-of-sample if we consider not just worst case (DRO) models but also best case (DOO) ones. We also show, however, that this comes at a cost: optimistic solutions are more sensitive to model error than either worst case or SAA optimizers and, hence, are less robust, and calibrating the worst or best case model to outperform SAA may be difficult when data are limited.