The Newsvendor with Advice

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.