Learning Preferences Under Noise and Loss Aversion: An Optimization Approach

Preference learning has been a topic of research in many fields, including operations research, marketing, machine learning, and behavioral economics. In this work, we strive to combine the ideas from these different fields into a single methodology to learn preferences and make decisions. We use robust and integer optimization in an adaptive and dynamic way to determine preferences from data that are consistent with human behavior. We use integer optimization to address human inconsistency, robust optimization and conditional value at risk (CVaR) to address loss aversion, and adaptive conjoint analysis and linear optimization to frame the questions to learn preferences. The paper makes the following methodological contributions: to the robust optimization literature by proposing a method to derive uncertainty sets from adaptive questionnaires, to the marketing literature by using the analytic center of discrete sets (as opposed to polyhedra) to capture errors and inconsistencies, and to the risk modeling literature by using efficient methods from computer science for sampling to optimize CVaR. We have implemented an online software that uses the proposed approach and report empirical evidence of its strength.