报告一

【时间地点】

报告时间：2023年12月18日，上午10:00-11:30

报告地点：西安交通大学兴庆校区数学楼2-1会议室

【报告题目】

Statistical Robustness of Stochastic Generalized Equations: Theory and Applications

【报告摘要】

Sample average approximation which is also known as Monte Carlo method has been widely used for solving stochastic programming and equilibrium problems. In a data-driven environment, samples are often drawn from empirical data which may be potentially contaminated. In that case, we are concerned with whether the statistical estimators obtained from solving the sample average approximate problems are statistically robust. There are at least two ways to proceed the research: one is to look into the sensitivity of the estimator with respect to a single data perturbation (outlier) via so-called influence function. The approach is widely known as robust statistics. The other is to consider the case where all data are potentially contaminated, and investigate how the difference between the laws of the statistical estimators based on contaminated data and real data (not contaminated) is controllable under some metrics. In this work, we use stochastic generalized equations as a unified framework and discuss how data contamination described above may affect the solutions of the SGE. Since the SGE may have multiple solutions, we use the proto-derivative of a set-valued mapping to introduce the notion of generalized influence function (GIF) of the solutions to the SGE and derive sufficient conditions under which the GIF is well defined, bounded and uniformly bounded. We then move on to analyze the solutions of the SGE when all of sample data are potentially contaminated, and demonstrate statistical robustness of the solutions obtained from solving sample average approximate SGE when perturbed data are in some appropriate topological structure. As an application, we discuss how this kind of analysis may be applied to machine learning. This talk is drawn from GRC project work (14204821) carried out jointly with Shaoyan Guo, Sainan Zhang, Hailin Sun and Manlan Li.

报告二

【时间地点】

报告时间：2023年12月20日，上午10:00-11:30

报告地点：西安交通大学创新港校区涵英楼5-10017会议室

【报告题目】

Random Utility Function and Distributionally Preference Robust Approach in Multiattribute Decision Making

【报告摘要】

Von Neumann-Morgenstern's expected utility theory uses a single deterministic utility function to describe a decision maker's preference relation over random prospects. The current research of preference robust optimization (PRO) deals with the case where the true utility function is unknown and the optimal decision is based on the worst-case utility function from an ambiguity set of plausible utility functions. In this talk, we consider multi-attribute decision making problems where the decision maker's preference can only be described by a random utility function but the probability distribution of the random utility is ambiguous. We propose a distributionally robust model where the worst probability distribution of the utility function instead of worst-case utility function is used in the optimal decision making to mitigate the risk arising from the ambiguity of information about the true utility. We concentrate on a class of piecewise linear random utility functions whose randomness is characterized by the utility increments of the linear piece over some specified intervals. Two approaches are subsequently proposed to construct the ambiguity set: one is to use sample mean and sample variance to construct an ambiguity set of the random parameters and the other is to use bootstrap studentized statistics and Tukey’s depth to construct a confidence region of the random parameters. We then move on to discuss tractable formulations of the DPRO models and carry out some numerical studies on the performance of the one based on the bootstrap approach. Finally, we extend the discussion to general continuous random utility functions. This work may be regarded as the first attempt of applying the well-known distributionally robust optimization approach to PRO models.  The talk is based on a recent joint work with Jian Hu (University of Michigan).

【报告专家简介】

Huifu Xu is a Professor of the Department of Systems Engineering and Engineering Management, The Chinese University of Hong Kong. Prior to joining CUHK in 2019, he was a professor of Operational Research in the School of Mathematical Sciences, University of Southampton. He received a PhD degree from University of Ballarat (Federation University Australia) in 1999 and worked as a postdoctoral research fellow in the Australian Graduate School of Management. Huifu Xu’s current research is on optimal decision making under uncertainty including preference robust optimization, distributionally robust optimization and risk analytics. He is currently an associate editor of Computational Management Science and Mathematical Programming.