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 simila...

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Veröffentlicht in:Journal of the American Statistical Association 2024-01, Vol.119 (545), p.552-564
Hauptverfasser: Fan, Jianqing, Guo, Yongyi, Yu, Mengxin
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Guo, Yongyi
Yu, Mengxin
description 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 ( T 2 m + 1 4 m − 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.
doi_str_mv 10.1080/01621459.2022.2128359
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source Taylor & Francis:Master (3349 titles)
subjects Contextual dynamic pricing
Decision making
Decision theory
Demand curves
Generalized linear model with unknown link
Generalized linear models
income
issues and policy
Linear analysis
linear models
Lower bounds
Market value
markets
Noise
Nonparametric statistics
Optimization
Policy optimization
Pricing
Product specifications
Regret
Statistical models
Statistics
Upper bounds
title Policy Optimization Using Semiparametric Models for Dynamic Pricing
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