  We consider a data-driven newsvendor problem, where one has access to past
demand data and the associated feature information. We solve the problem by
estimating the target quantile function using a deep neural network (DNN). The
remarkable representational power of DNN allows our framework to incorporate or
approximate various extant data-driven models. We provide theoretical
guarantees in terms of excess risk bounds for the DNN solution characterized by
the network structure and sample size in a non-asymptotic manner, which justify
the applicability of DNNs in the relevant contexts. Specifically, the
convergence rate of the excess risk bound with respect to the sample size
increases in the smoothness of the target quantile function but decreases in
the dimension of feature variables. This rate can be further accelerated when
the target function possesses a composite structure. Compared to other typical
models, the nonparametric DNN method can effectively avoid or significantly
reduce the model misspecification error. In particular, our theoretical
framework can be extended to accommodate the data-dependent scenarios, where
the data-generating process is time-dependent but not necessarily identical
over time. Finally, we apply the DNN method to a real-world dataset obtained
from a food supermarket. Our numerical experiments demonstrate that (1) the DNN
method consistently outperforms other alternatives across a wide range of cost
parameters, and (2) it also exhibits good performance when the sample size is
either very large or relatively limited.
