Policy Optimization Using Semiparametric Models for Dynamic Pricing

In this article, we study the contextual dynamic pricing problem where the market value of a product is linear in its observed features plus some market noise. Products are sold one at a time, and only a binary response indicating success or failure of a sale is observed. Our model setting is similar to the work by? except that we expand the demand curve to a semiparametric model and learn dynamically both parametric and nonparametric components. We propose a dynamic statistical learning and decision making policy that minimizes regret (maximizes revenue) by combining semiparametric estimation for a generalized linear model with unknown link and online decision making. Under mild conditions, for a market noise cdf (Formula presented.) with mth order derivative ((Formula presented.)), our policy achieves a regret upper bound of (Formula presented.), where T is the time horizon and (Formula presented.) is the order hiding logarithmic terms and the feature dimension d. The upper bound is further reduced to (Formula presented.) if F is super smooth. These upper bounds are close to (Formula presented.), the lower bound where F belongs to a parametric class. We further generalize these results to the case with dynamic dependent product features under the strong mixing condition. Supplementary materials for this article are available online.