上海治理论坛第400期（范薇薇副教授，，，，，，同济大学）

题    目：数据价值：一种鲁棒线性妄想要领Value of Data: A Robust Linear Programming Approach

演 讲 人：范薇薇，，，，，，同济大学副教授

主 持 人：镇  璐，，，，，，8188cc威尼斯治理学院教授

时    间：2019年9月25日（周三），，，，，，下昼1:30

地    点：校本部东区治理学院467室

主理单位：8188cc威尼斯治理学院、8188cc威尼斯治理学院青年西席联谊会

演讲人简介：

范薇薇，，，，，，同济大学治理高等研究院副教授。。。之前曾任中国科学手艺大学助理教授。。。2015年结业于香港科技大学，，，，，，获得博士学位；；；；2011年本科结业于中科大数学系。。。主要研究偏向包括：仿真优化，，，，，，鲁棒优化，，，，，，以及它们在医疗方面的应用。。。主持国家青年科学基金项目，，，，，，在《Operations Research》，，，，，，《Management Science》等国际顶级期刊上揭晓多篇学术论文。。。

演讲内容简介：

Linear programming (LP) is a widely used tool in the decision-making processes. In practice, the associated parameters are often unknown and the key issue becomes how to interpret these parameters with the real-world data. There are two commonly used approaches. When the unknown parameters only appear in the objective, the point estimation approach is often adopted. This approach estimates the parameters by using statistical methods and then plugs the estimated parameters into the original problem. Consequently, the estimated LP is solved as a surrogate. When the unknown parameters appear in the constraints, the robust optimization approach is often adopted. This approach constructs an uncertainty set for the parameters and then optimizes the objective over the uncertainty set. However, both approaches may yield a large discrepancy from the nominal optimal objective and we call this discrepancy the regret. It is easy to see that both the regret mainly hinges on the data set used to estimate the parameters or construct the uncertainty set. To study the impact of data set, we propose a novel framework that is able to construct the con?dence intervals for both types of regrets as a function of data set, respectively. We ?nd that the regrets (or the widths of con?dence interval) shrink to zero at an order of n-1/2, where n refers to the volume of data set. Furthermore, we design a two-stage procedure to determine the minimal volume of data set required for a prescribed level of regrets.

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