The Nonstationary Newsvendor with (and without) Predictions
Lin An, Andrew A. Li, Benjamin Moseley, R. Ravi
TL;DR
This work tackles sequential inventory decisions under unknown, nonstationary demand through a formal Nonstationary Newsvendor model with a variation parameter $v\in[0,1]$ and optional generic predictions with accuracy exponent $a$. It delivers a complete theoretical treatment for the no-prediction setting, proving a minimax lower bound $\Omega(T^{(3+v)/4})$ and an algorithm with matching upper bound $\tilde{O}(T^{(3+v)/4})$, even when $v$ is unknown, by using fixed-time or shrinking windows. It then extends to a prediction-augmented setting, introducing the Prediction-Error-Robust Policy (PERP) that robustly leverages predictions without knowing their accuracy and achieves $\tilde{O}(T^{\min\{(3+v)/4, a\}})$ regret when $v$ is known, with lower bounds showing limits when both $v$ and $a$ are unknown. Empirical results on three real datasets (Wikipedia, Rossmann, and a Japanese restaurant) demonstrate that PERP closes a substantial portion of the gap between prediction-free and prediction-based baselines, highlighting practical value in dynamic, uncertain environments. Overall, the paper advances online inventory optimization under nonstationarity by jointly optimizing for unknown demand evolution and potentially noisy predictions, yielding provable regret guarantees and robust real-world performance.
Abstract
The classic newsvendor model yields an optimal decision for a ``newsvendor'' selecting a quantity of inventory, under the assumption that the demand is drawn from a known distribution. Motivated by applications such as cloud provisioning and staffing, we consider a setting in which newsvendor-type decisions must be made sequentially, in the face of demand drawn from a stochastic process that is both unknown and nonstationary. All prior work on this problem either (a) assumes that the level of nonstationarity is known, or (b) imposes additional statistical assumptions that enable accurate predictions of the unknown demand. Our research tackles the Nonstationary Newsvendor without these assumptions, both with and without predictions. We first, in the setting without predictions, design a policy which we prove achieves order-optimal regret -- ours is the first policy to accomplish this without being given the level of nonstationarity of the underlying demand. We then, for the first time, introduce a model for generic (i.e. with no statistical assumptions) predictions with arbitrary accuracy, and propose a policy that incorporates these predictions without being given their accuracy. We upper bound the regret of this policy, and show that it matches the best achievable regret had the accuracy of the predictions been known. Our findings provide valuable insights on inventory management. Managers can make more informed and effective decisions in dynamic environments, reducing costs and enhancing service levels despite uncertain demand patterns. We empirically validate our new policy with experiments based on three real-world datasets containing thousands of time-series, showing that it succeeds in closing approximately 74% of the gap between the best approaches based on nonstationarity and predictions alone.