CORMSIS Seminar "Random Utility Function and Distributionally Preference Robust Approach in Multiattribute Decision Making", by Professor Huifu Xu (The Chinese University of Hong Kong) Event

Event details

Abstract: 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 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 bootstrap approach. Finally, we extend to the discussions to the 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 – Dearborn), Dali Zhang (Shanghai Jiao Tong University) and Sainan Zhang (The Chinese University of Hong Kong).