Policy Optimization Using Semiparametric Models for Dynamic Pricing

Jianqing Fan, Yongyi Guo and Mengxin Yu

Journal of the American Statistical Association, 2024, vol. 119, issue 545, 552-564

Abstract: 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 F(·) with mth 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. Supplementary materials for this article are available online.

Date: 2024
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Working Paper: Policy Optimization Using Semi-parametric Models for Dynamic Pricing (2022)
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DOI: 10.1080/01621459.2022.2128359

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