# Revealed Preference at Scale: Learning Personalized Preferences from Assortment Choices

arXiv: https://arxiv.org/abs/1509.05113 · HTML: https://mlsanity.com/paper/1509.05113/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 17 Sep 2015.

## Built on by (most cited first, 4 of 4)

- [Inverse Reinforcement Learning with Just Classification and a Few Regressions](https://mlsanity.com/paper/2509.21172/) (2025)
- [Incentivizing Efficient Equilibria in Traffic Networks with Mixed Autonomy](https://mlsanity.com/paper/2106.04678/) (2021)
- [The Value of Personalized Recommendations: Evidence from Netflix](https://mlsanity.com/paper/2511.07280/) (2025)
- [Learning Preference from Observed Rankings](https://mlsanity.com/paper/2602.16476/) (2026)

## Abstract (arXiv)

We consider the problem of learning the preferences of a heterogeneous population by observing choices from an assortment of products, ads, or other offerings. Our observation model takes a form common in assortment planning applications: each arriving customer is offered an assortment consisting of a subset of all possible offerings; we observe only the assortment and the customer's single choice. In this paper we propose a mixture choice model with a natural underlying low-dimensional structure, and show how to estimate its parameters. In our model, the preferences of each customer or segment follow a separate parametric choice model, but the underlying structure of these parameters over all the models has low dimension. We show that a nuclear-norm regularized maximum likelihood estimator can learn the preferences of all customers using a number of observations much smaller than the number of item-customer combinations. This result shows the potential for structural assumptions to speed up learning and improve revenues in assortment planning and customization. We provide a specialized factored gradient descent algorithm and study the success of the approach empirically.