A distributionally robust optimization framework for attribute-independent preference estimation

In this paper, we introduced a framework that requires only choice data to learn a decision-maker's utility, unlike the classic random utility framework which needs historical choices and multiple attributes. We proposed a two-stage optimization model for the single decision-maker's discrete choice processes with sequential uncertainties. In the first stage, the decision-maker made a strategic choice that stochastically determined the set of future alternatives. In the second stage, after these alternatives were realized, the decision-maker made a final operational choice to maximize utility. The second stage was modeled as a distributionally robust optimization problem with a Kullback–Leibler divergence constraint, enabling worst-case utility evaluation. This model built an ambiguity set from historical choice data to define possible distributions for the decision-maker's preferences. We also analyzed the problem's convexity and used an augmented Lagrangian algorithm to find the optimal solution. Extensive numerical experiments, including case studies and in-depth sensitivity analyses, demonstrated the method's effectiveness.