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.
All Science Journal Classification (ASJC) codes
- Statistics and Probability
- Statistics, Probability and Uncertainty
- Contextual dynamic pricing
- Generalized linear model with unknown link
- Nonparametric statistics
- Policy optimization