Data-driven learning in dynamic pricing using adaptive optimization

We consider the pricing problem faced by a retailer endowed with a finite inventory of a product offered over a finite planning horizon in an environment where customers are price-sensitive. The parameters of the product demand curve are fixed but unknown to the seller who only has at his disposal a history of sales data. We propose an adaptive optimization approach to setting prices that captures the ability of the seller to exploit information gained as a byproduct of pricing in his quest to maximize revenues. We construct data-driven uncertainty sets that encode the beliefs of the retailer about the demand curve parameters. We capture the ability of the retailer to explore the characteristics of customer behavior by allowing the uncertainty set to depend on the pricing decisions. We model his capacity to exploit the information dynamically acquired by letting the pricing decisions adapt to the history of observations. These modeling features enable us to unify optimization and estimation as the uncertainty set is updated “on-the-fly”, during optimization. We propose a hierarchical approximation scheme for the resulting adaptive optimization problem with decision-dependent uncertainty set which yields a practically tractable mixed-binary conic optimization problem. We discuss several variants and extensions of our model that illustrate the versatility of the proposed method. We present computational results that show that the proposed policies: (a) yield higher profits compared to commonly used policies, (b) nearly match perfect information results with respect to downside measures such as the Conditional Value-at-Risk, and (c) can be obtained in modest computational time for large-scale problems.