  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. We derive an upper bound on the
generalization error of RUMnets fitted on choice data, and gain theoretical
insights on their ability to predict choices on new, unseen data depending on
critical parameters of the dataset and architecture. By leveraging open-source
libraries for 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.
