基于学习的鲁棒Optimization：过程和统计保证
Learning-based Robust Optimization: Procedures and Statistical Guarantees
摘要：
鲁棒优化（Robust optimization，RO）是求解不确定约束最优化问题的一种常用方法。在本文中，我们研究了一个统计框架，将数据集成到RO中，基于使用与已建立的RO工具兼容的几何形状（组合）学习预测集，以及实现有限样本非参数统计保证可行性的简单数据分割验证步骤。我们证明了我们所需的样本量，以实现在给定的置信水平的可行性是独立的决策空间和概率空间的随机性的尺寸，并讨论了一些方法来提高客观性能，同时保持这些无量纲的统计可行性保证。
英文摘要：
Robust optimization (RO) is a common approach to tractably obtain safeguarding solutions for optimization problems with uncertain constraints. In this paper, we study a statistical framework to integrate data into RO, based on learning a prediction set using (combinations of) geometric shapes that are compatible with established RO tools, and a simple data-splitting validation step that achieves finite-sample nonparametric statistical guarantees on feasibility. We demonstrate how our required sample size to achieve feasibility at a given confidence level is independent of the dimensions of both the decision space and the probability space governing the stochasticity, and discuss some approaches to improve the objective performances while maintaining these dimension-free statistical feasibility guarantees.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
