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The standard newsvendor model assumes a stochastic demand distribution as
well as costs for overages and underages. The celebrated critical fractile
formula can be used to determine the optimal inventory levels. While the model
has been leveraged in numerous applications, often in practice more
characteristics and features of the problem are known. Using these features, it
is common to employ machine learning to predict inventory levels over the
classic newsvendor approach.
An emerging line of work has shown how to use incorporate machine learned
predictions into models to circumvent lower bounds and give improved
performance. This paper develops the first newsvendor model that incorporates
machine learned predictions. The paper considers a repeated newsvendor setting
with nonstationary demand. There is a prediction is for each period's demand
and, as is the case in machine learning, the prediction can be noisy. The goal
is for an inventory management algorithm to take advantage of the prediction
when it is high quality and to have performance bounded by the best possible
algorithm without a prediction when the prediction is highly inaccurate.
This paper proposes a generic model of a nonstationary newsvendor without
predictions and develops optimal upper and lower bounds on the regret. The
paper then propose an algorithm that takes a prediction as advice which,
without a priori knowledge of the accuracy of the advice, achieves the nearly
optimal minimax regret. The perforamce mataches the best possible had the
accuracy been known in advance. We show the theory is predictive of practice on
real data and demonstrtate emprically that our algorithm has a 14% to 19% lower
cost than a clairvoyant who knows the quality of the advice beforehand.
