Robust Dynamic Pricing with Demand Learning in the Presence of Outlier Customers

This paper studies a dynamic pricing problem under model misspecification. To characterize model misspecification, we adopt the ε -contamination model—the most fundamental model in robust statistics and machine learning. In particular, for a selling horizon of length T , the online ε -contamination model assumes that demands are realized according to a typical unknown demand function only for ( 1 − ε ) T periods. For the rest of ε T periods, an outlier purchase can happen with arbitrary demand functions. The challenges brought by the presence of outlier customers are mainly due to the fact that arrivals of outliers and their exhibited demand behaviors are completely arbitrary, therefore calling for robust estimation and exploration strategies that can handle any outlier arrival and demand patterns. We first consider unconstrained dynamic pricing without any inventory constraint. In this case, we adopt the Follow-the-Regularized-Leader algorithm to hedge against outlier purchase behavior. Then, we introduce inventory constraints. When the inventory is insufficient, we study a robust bisection-search algorithm to identify the clearance price—that is, the price at which the initial inventory is expected to clear at the end of T periods. Finally, we study the general dynamic pricing case, where a retailer has no clue whether the inventory is sufficient or not. In this case, we design a meta-algorithm that combines the previous two policies. All algorithms are fully adaptive, without requiring prior knowledge of the outlier proportion parameter ε . Simulation study shows that our policy outperforms existing policies in the literature.