Optimal Robust Policy for Feature-Based Newsvendor

• 成果类型: Article; Early Access
• 署名作者: Zhang, Luhao; Yang, Jincheng; Gao, Rui
• 署名单位: University of Texas System; University of Texas Austin; University of Texas System; University of Texas Austin
• 刊物名称: MANAGEMENT SCIENCE
• ISSN/ISSBN: 0025-1909
• DOI: 10.1287/mnsc.2023.4810
• 发表日期: 2023
• 关键词: side information; contextual decision making; Inventory management; adjustable robust optimization

摘要

We study policy optimization for the feature-based newsvendor, which seeks an end-to-end policy that renders an explicit mapping from features to ordering decisions. Most existing works restrict the policies to some parametric class that may suffer from sub -optimality (such as affine class) or lack of interpretability (such as neural networks). Differ-ently, we aim to optimize over all functions of features. In this case, the classic empirical risk minimization yields a policy that is not well-defined on unseen feature values. To avoid such degeneracy, we consider a Wasserstein distributionally robust framework. This leads to an adjustable robust optimization, whose optimal solutions are notoriously diffi-cult to obtain except for a few notable cases. Perhaps surprisingly, we identify a new class of policies that are proven to be exactly optimal and can be computed efficiently. The opti-mal robust policy is obtained by extending an optimal robust in-sample policy to unob-served feature values in a particular way and can be interpreted as a Lipschitz regularized critical fractile of the empirical conditional demand distribution. We compare our method with several benchmarks using synthetic and real data and demonstrate its superior empir-ical performance.