Applied Math Seminar- Utility Preference Robust Optimization with Moment-Type Information Structure

Speaker: Dr. Sainan Zhang, Department of Decision Sciences, George Washington University.

Date and Time: Friday, November 8, 2024 2pm-3pm

 

Place: Phillips 730

 

Title: Utility Preference Robust Optimization with Moment-Type Information Structure

 

Abstract: Utility preference robust optimization (PRO) models have recently been proposed to deal with decision-making problems where the decision-maker’s true utility function is unknown and the optimal decision is based on the worst-case utility function in an ambiguity set of utility functions. In this paper, we consider the case where the ambiguity set is constructed using some moment-type conditions. We propose piecewise linear approximation of the utility functions in the ambiguity set. The approximate maximin problem can be solved directly by derivative-free methods when the utility functions are nonconcave. Alternatively, we can reformulate the approximate problem as a single mixed integer linear program (MILP) and solve the MILP by existing solvers such as Gurobi. To justify the approximation scheme, we derive error bounds for the approximate ambiguity set, the optimal value and optimal solutions of the approximate maximin problem. To address the data perturbation/contamination issues arising from the construction of the ambiguity set, we derive some stability results which quantify the variation of the ambiguity set against perturbations in the elicitation data and its propagation to the optimal value and optimal solutions of the PRO model. Moreover, we extend the PRO models to allow some inconsistencies in the process of eliciting the decision-maker’s preferences. Finally, we carry out numerical tests to evaluate the performances of the proposed numerical schemes and show that the computational schemes work fairly efficiently, the PRO model is resilient against small perturbations in data (with respect to both exogenous uncertainty data and preference elicitation data), and there is a potential to improve the efficiency of the preference elicitation by incorporating an optimal selection strategy.