Risk-Adaptive Local Decision Rules

• 成果类型: Article
• 署名作者: Royset, Johannes O.; Lejeune, Miguel A.
• 署名单位: University of Southern California; George Washington University
• 刊物名称: OPERATIONS RESEARCH
• ISSN/ISSBN: 0030-364X
• DOI: 10.1287/opre.2023.0564
• 发表日期: 2025
• 页码: 2125-2145
• 关键词: Robust Optimization; affine policies; tilt stability; ADAPTABILITY; optimality; calmness; DESIGN

摘要

For parameterized mixed-binary optimization problems, we construct local decision rules that prescribe near-optimal courses of action across a set of parameter values. The decision rules stem from solving risk-adaptive training problems over classes of continuous, possibly nonlinear mappings. In asymptotic and nonasymptotic analysis, we establish that the decision rules prescribe near-optimal decisions locally for the actual problems without relying on linearity, convexity, or smoothness. The development also accounts for practically important aspects such as inexact function evaluations, solution tolerances in training problems, regularization, and reformulations to solver-friendly models. The decision rules also furnish a means to carry out sensitivity and stability analysis for broad classes of parameterized optimization problems. We develop a decomposition algorithm for solving the resulting training problems and demonstrate its ability to generate quality decision rules on a nonlinear binary optimization model from search theory.