Policy Optimization Using Semiparametric Models for Dynamic Pricing

In this paper, 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 Javanmard and Nazerzadeh (2019) 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 c.d.f. F(·) with m-th order derivative (m≥2), our policy achieves a regret upper bound of O˜d(T2m+14m−1), where T is the time horizon and O˜d is the order hiding logarithmic terms and the feature dimension d. The upper bound is further reduced to O˜d(T) if F is super smooth. These upper bounds are close to Ω(T), 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.