  Models of choice are a fundamental input to many now-canonical optimization
problems in the field of Operations Management, including assortment,
inventory, and price optimization. Naturally, accurate estimation of these
models from data is a critical step in the application of these optimization
problems in practice. Concurrently, recent advancements in deep learning have
sparked interest in integrating these techniques into choice modeling. However,
there is a noticeable research gap at the intersection of deep learning and
choice modeling, particularly with both theoretical and empirical foundations.
Thus motivated, we first propose a choice model that is the first to
successfully (both theoretically and practically) leverage a modern neural
network architectural concept (self-attention). Theoretically, we show that our
attention-based choice model is a low-rank generalization of the Halo
Multinomial Logit (Halo-MNL) model. We prove that whereas the Halo-MNL requires
$\Omega(m^2)$ data samples to estimate, where $m$ is the number of products,
our model supports a natural nonconvex estimator (in particular, that which a
standard neural network implementation would apply) which admits a near-optimal
stationary point with $O(m)$ samples. Additionally, we establish the first
realistic-scale benchmark for choice model estimation on real data, conducting
the most extensive evaluation of existing models to date, thereby highlighting
our model's superior performance.
