Revealed Preference at Scale: Learning Personalized Preferences from Assortment Choices

TL;DR

This paper introduces a low-dimensional mixture choice model for learning personalized preferences from assortment choices, demonstrating that structural assumptions enable efficient estimation with fewer observations, benefiting assortment planning.

Contribution

It proposes a nuclear-norm regularized maximum likelihood estimator for low-dimensional preference learning in heterogeneous populations, with an efficient algorithm and empirical validation.

Findings

The model accurately learns preferences with fewer observations.

Structural assumptions improve learning efficiency.

Empirical results validate the approach's effectiveness.

Abstract

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.