# Representing Random Utility Choice Models with Neural Networks

arXiv: https://arxiv.org/abs/2207.12877 · HTML: https://mlsanity.com/paper/2207.12877/

## Key facts

- Cited by 13 papers in the map (data through 14 Oct 2026).
- Builds on 4 of its 39 references that are in the map.
- First posted on arXiv 26 Jul 2022.

## Builds on (most cited first, 4 of 4)

- [A vector-contraction inequality for Rademacher complexities](https://mlsanity.com/paper/1605.00251/) (2016)
- [Theory-based residual neural networks: A synergy of discrete choice models and deep neural networks](https://mlsanity.com/paper/2010.11644/) (2020)
- [Predicting Choice with Set-Dependent Aggregation](https://mlsanity.com/paper/1906.06365/) (2019)
- [Decision Forest: A Nonparametric Approach to Modeling Irrational Choice](https://mlsanity.com/paper/1904.11532/) (2019)

## Built on by (most cited first, 13 of 13)

- [Transformer Choice Net: A Transformer Neural Network for Choice Prediction](https://mlsanity.com/paper/2310.08716/) (2023)
- [Deep Learning for Choice Modeling](https://mlsanity.com/paper/2208.09325/) (2022)
- [A Neural Network Based Choice Model for Assortment Optimization](https://mlsanity.com/paper/2308.05617/) (2023)
- [A Nonparametric Approach with Marginals for Modeling Consumer Choice](https://mlsanity.com/paper/2208.06115/) (2022)
- [Choice Models and Permutation Invariance: Demand Estimation in Differentiated Products Markets](https://mlsanity.com/paper/2307.07090/) (2023)
- [Modeling Choice via Self-Attention](https://mlsanity.com/paper/2311.07607/) (2023)
- [DeepHalo: A Neural Choice Model with Controllable Context Effects](https://mlsanity.com/paper/2601.04616/) (2026)
- [From Small to Large: A Graph Convolutional Network Approach for Solving Assortment Optimization Problems](https://mlsanity.com/paper/2507.10834/) (2025)
- [Constrained Triple-Head Price Optimization (C3PO) Network for Discrete-Choice Models](https://mlsanity.com/paper/2605.06941/) (2026)
- [Tabular Foundation Models for Discrete Choice Estimation](https://mlsanity.com/paper/2607.13314/) (2026)
- [Consideration Circuits: Depth Separation and Universality Beyond a Single Softmax](https://mlsanity.com/paper/2610.04143/) (2026)
- [Logic-Logit: A Logic-Based Approach to Choice Modeling](https://mlsanity.com/paper/2610.05501/) (2026)
- [Better Capturing Interactions Between Products in~Retail: Revisited Negative Sampling for~Basket Choice Modeling](https://mlsanity.com/paper/2610.17963/) (2026)

## Abstract (arXiv)

Motivated by the successes of deep learning, we propose a class of neural network-based discrete choice models, called RUMnets, inspired by the random utility maximization (RUM) framework. This model formulates the agents' random utility function using a sample average approximation. We show that RUMnets sharply approximate the class of RUM discrete choice models: any model derived from random utility maximization has choice probabilities that can be approximated arbitrarily closely by a RUMnet. Reciprocally, any RUMnet is consistent with the RUM principle. Our approach is closely related to ranking-based models and mixtures of multinomial logits proposed in previous literature, in a more general contextual setting. We derive an upper bound on the generalization error of RUMnets fitted on choice data, and provide theoretical insights on their ability to predict choices on new, unseen data depending on critical parameters of the dataset and architecture. The models are estimated by leveraging open-source libraries for training neural networks. We find that RUMnets are competitive against several choice modeling and machine learning methods in terms of predictive accuracy on two real-world datasets. We also conduct synthetic experiments that isolate the effects of each component of the architecture.