  The emergence of Big Data has enabled new research perspectives in the
discrete choice community. While the techniques to estimate Machine Learning
models on a massive amount of data are well established, these have not yet
been fully explored for the estimation of statistical Discrete Choice Models
based on the random utility framework. In this article, we provide new ways of
dealing with large datasets in the context of Discrete Choice Models. We
achieve this by proposing new efficient stochastic optimization algorithms and
extensively testing them alongside existing approaches. We develop these
algorithms based on three main contributions: the use of a stochastic Hessian,
the modification of the batch size, and a change of optimization algorithm
depending on the batch size. A comprehensive experimental comparison of fifteen
optimization algorithms is conducted across ten benchmark Discrete Choice Model
cases. The results indicate that the HAMABS algorithm, a hybrid adaptive batch
size stochastic method, is the best performing algorithm across the
optimization benchmarks. This algorithm speeds up the optimization time by a
factor of 23 on the largest model compared to existing algorithms used in
practice. The integration of the new algorithms in Discrete Choice Models
estimation software will significantly reduce the time required for model
estimation and therefore enable researchers and practitioners to explore new
approaches for the specification of choice models.
