Constrained Triple-Head Price Optimization (C3PO) Network for Discrete-Choice Models
Abstract
We propose a Constrained Triple-Head Price Optimization (C3PO) network for real-time bi-level decision making in discrete-choice environments. In these settings, a seller selects product or service offerings to achieve business objectives, while heterogeneous users make personalized acceptance or rejection decisions based on their preferences, ultimately determining seller outcomes. Existing approaches that fine-tune pre-trained tabular foundation models on synthetic data are limited by their imitation-learning paradigm and inability to enforce common pricing rules, including cross-product and global constraints. C3PO addresses these limitations through a novel transformer-based architecture that jointly integrates price imitation learning, multi-task revenue prediction, and in-context elasticity learning to generate robust pricing recommendations across domains without retraining. A lightweight differentiable constraint layer enables generated prices to satisfy business constraints while optimizing the revenue objective. We demonstrate strong out-of-distribution performance on simulated, synthetic, and real-world datasets. Across simulated benchmarks where the calibrated MNL model is misspecified relative to the ground-truth choice model, C3PO improves expected revenue by 1.4 to 7.9 percentage points over a calibrated MNL baseline. The constraint layer reduces average absolute constraint violations by more than 50\%. We further deploy the model in real-world applications, including healthcare tender pricing and airline ancillary pricing, where C3PO improves directional pricing effectiveness, measured by price-increase and price-decrease recall, by 18--34 percentage points depending on the baselines considered, including calibrated MNL, classical optimization, and off-the-shelf tabular foundation-models.
Related
- Discrete-time feedback linearization control for nonsmooth constrained optimization
- From Inverse Problems to Adjoint Gradients: A Discrete, Implementation-Oriented Tutorial on PDE-Constrained Optimization
- Self-Consistent Adjoint Policy Iteration for Constrained Dynamic Portfolio Choice
- Scalable Pontryagin-Guided Adjoint-to-Control Recovery for Constrained Dynamic Portfolio Choice
- Symmetry-breaking in a discrete-choice LQG mean field game
BibTeX
@misc{subramanian2026constrained,
title = {{Constrained Triple-Head Price Optimization (C3PO) Network for Discrete-Choice Models}},
author = {Shivaram Subramanian and Zhengliang Xue and Markus Ettl and Yingdong Lu and Jayant Kalagnanam},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2605.06941},
eprint = {2605.06941},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2605.06941},
}
RIS
TY - UNPB
TI - Constrained Triple-Head Price Optimization (C3PO) Network for Discrete-Choice Models
AU - Shivaram Subramanian
AU - Zhengliang Xue
AU - Markus Ettl
AU - Yingdong Lu
AU - Jayant Kalagnanam
PY - 2026
DA - 2026/10/08
PB - arXiv
DO - 10.48550/arxiv.2605.06941
UR - https://arxiv.org/abs/2605.06941
AB - We propose a Constrained Triple-Head Price Optimization (C3PO) network for real-time bi-level decision making in discrete-choice environments. In these settings, a seller selects product or service offerings to achieve business objectives, while heterogeneous users make personalized acceptance or rejection decisions based on their preferences, ultimately determining seller outcomes. Existing approaches that fine-tune pre-trained tabular foundation models on synthetic data are limited by their imitation-learning paradigm and inability to enforce common pricing rules, including cross-product and global constraints. C3PO addresses these limitations through a novel transformer-based architecture that jointly integrates price imitation learning, multi-task revenue prediction, and in-context elasticity learning to generate robust pricing recommendations across domains without retraining. A lightweight differentiable constraint layer enables generated prices to satisfy business constraints while optimizing the revenue objective. We demonstrate strong out-of-distribution performance on simulated, synthetic, and real-world datasets. Across simulated benchmarks where the calibrated MNL model is misspecified relative to the ground-truth choice model, C3PO improves expected revenue by 1.4 to 7.9 percentage points over a calibrated MNL baseline. The constraint layer reduces average absolute constraint violations by more than 50\%. We further deploy the model in real-world applications, including healthcare tender pricing and airline ancillary pricing, where C3PO improves directional pricing effectiveness, measured by price-increase and price-decrease recall, by 18--34 percentage points depending on the baselines considered, including calibrated MNL, classical optimization, and off-the-shelf tabular foundation-models.
ER -