Data-Driven Inventory Control with Shifting Demand

We consider an inventory control problem with lost-sales in a shifting demand environment. Over a planning horizon of T periods, demand distributions can change up to O( log T) times, but the firm does not know the demand distributions before or after each change, the time periods when changes occur, or the number of changes. Therefore, the firm needs to detect changes and learn the demand distributions only from historical sales data. We show that with censored demand, active exploration in the inventory space is needed for a reasonable detecting and learning algorithm. We provide a theoretical lower bound by partitioning all admissible policies into either exploration-heavy or exploitation-heavy, and for both categories we prove that the convergence rate cannot be better than omega(T). We then develop a nonparametric learning algorithm for this problem and prove that it achieves a convergence rate that (almost) matches the theoretical lower bound.