A Primal-dual Learning Algorithm for Personalized Dynamic Pricing with an Inventory Constraint
This addresses the challenge for firms in optimizing revenue through personalized pricing under unknown demand and inventory limits, representing a novel algorithmic design for resource-constrained learning problems.
The paper tackles the problem of personalized dynamic pricing with inventory constraints by developing a learning algorithm that is near-optimal as demand and capacity scale proportionally, achieving a regret rate independent of the number of consumer types.
We consider the problem of a firm seeking to use personalized pricing to sell an exogenously given stock of a product over a finite selling horizon to different consumer types. We assume that the type of an arriving consumer can be observed but the demand function associated with each type is initially unknown. The firm sets personalized prices dynamically for each type and attempts to maximize the revenue over the season. We provide a learning algorithm that is near-optimal when the demand and capacity scale in proportion. The algorithm utilizes the primal-dual formulation of the problem and learns the dual optimal solution explicitly. It allows the algorithm to overcome the curse of dimensionality (the rate of regret is independent of the number of types) and sheds light on novel algorithmic designs for learning problems with resource constraints.