Adaptive Preference Elicitation in Preference Robust CPT-Based Shortfall
Abstract
This paper investigates the cumulative prospect theory (CPT)-based shortfall risk measure where the value (utility) function and the distortion (probability weighting) functions are ambiguous. We propose a worst-case CPT-based shortfall risk measure where the capital requirement is based on the worst-case value function and distortion functions from an ambiguity set constructed with user-specific information (e.g., preference between risky and certain lotteries) and well-known general information such as the S-shape of the value functions. When the underlying random loss is discretely distributed and parameters in pairs of lotteries remain undetermined, we demonstrate that the worst-case value function and the distortion functions have a piecewise linear structure. Based on this observation, we develop an adaptive preference elicitation approach extended from the well-known polyhedral method to simultaneously elicit the distortion functions and the positive and negative parts of the value function by solving a sequence of mixed-integer linear programs. Based on the elicited distortions, we design new queries to construct a feasible set of the holistic value functions. The proposed framework iteratively shrinks the ambiguity set through designed queries, yielding a computationally implementable robust CPT-based shortfall risk measure. To examine the in-sample and out-of-sample performance of the elicited CPT-based preference functions and the resulting preference robust shortfall risk measure, we conduct numerical experiments under an S-shaped value function and inverse S-shaped distortion functions and report the corresponding results.
Related
- Adaptive pairwise preference elicitation for decision support: identifying the best alternative with fewer judgments
- Bayesian Deck-of-cards-based Ordinal Regression with Sequential Preference Elicitation
- Simulated Annealing for Model‐Robust Partial Profile Choice Designs in Healthcare Preference Studies
- Robust Direct Preference Optimization under Preference Label-Flip Attacks
- Reliability-Weighted Direct Preference Optimization: Penalized Weights for Robust Preference Learning
BibTeX
@misc{zhang2026adaptive,
title = {{Adaptive Preference Elicitation in Preference Robust CPT-Based Shortfall}},
author = {Sainan Zhang and Erick Delage and Huifu Xu},
howpublished = {arXiv},
year = {2026},
month = nov,
doi = {10.48550/arxiv.2611.02059},
eprint = {2611.02059},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2611.02059},
}
RIS
TY - UNPB
TI - Adaptive Preference Elicitation in Preference Robust CPT-Based Shortfall
AU - Sainan Zhang
AU - Erick Delage
AU - Huifu Xu
PY - 2026
DA - 2026/11/01
PB - arXiv
DO - 10.48550/arxiv.2611.02059
UR - https://arxiv.org/abs/2611.02059
AB - This paper investigates the cumulative prospect theory (CPT)-based shortfall risk measure where the value (utility) function and the distortion (probability weighting) functions are ambiguous. We propose a worst-case CPT-based shortfall risk measure where the capital requirement is based on the worst-case value function and distortion functions from an ambiguity set constructed with user-specific information (e.g., preference between risky and certain lotteries) and well-known general information such as the S-shape of the value functions. When the underlying random loss is discretely distributed and parameters in pairs of lotteries remain undetermined, we demonstrate that the worst-case value function and the distortion functions have a piecewise linear structure. Based on this observation, we develop an adaptive preference elicitation approach extended from the well-known polyhedral method to simultaneously elicit the distortion functions and the positive and negative parts of the value function by solving a sequence of mixed-integer linear programs. Based on the elicited distortions, we design new queries to construct a feasible set of the holistic value functions. The proposed framework iteratively shrinks the ambiguity set through designed queries, yielding a computationally implementable robust CPT-based shortfall risk measure. To examine the in-sample and out-of-sample performance of the elicited CPT-based preference functions and the resulting preference robust shortfall risk measure, we conduct numerical experiments under an S-shaped value function and inverse S-shaped distortion functions and report the corresponding results.
ER -