Policy Optimization Using Semiparametric Models for Dynamic Pricing
Policy Optimization Using Semiparametric Models for Dynamic Pricing
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DOI：
10.1080/01621459.2022.2128359
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发表时间：
2021-09
期刊：
影响因子：
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通讯作者：
Jianqing Fan;Yongyi Guo;Mengxin Yu
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文献类型：
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作者：
Jianqing Fan;Yongyi Guo;Mengxin Yu
摘要在这篇文章中，我们研究了上下文动态定价问题，其中产品的市场价值在其观察到的特征中是线性的，加上一些市场噪音。每次销售一个产品，并且仅观察到指示销售成功或失败的二进制响应。我们的模型设置是类似的工作？不同的是，我们将需求曲线扩展为半参数模型，并动态地学习参数和非参数分量。我们提出了一个动态的统计学习和决策政策，最大限度地减少遗憾（最大限度地提高收入），通过结合半参数估计的广义线性模型与未知的链接和在线决策。在温和的条件下，对于具有m阶导数（m≥2）的市场噪声cdf F（·），我们的策略达到了O d（T2m+14m−1）的后悔上界，其中T是时间范围，O d是隐藏对数项的阶数和特征维数d。如果F是超光滑的，则上界进一步降为O d（T）。这些上界接近于Ω（T），即F属于参数类的下界。我们进一步将这些结果推广到强混合条件下的动态相关乘积特征的情形。本文的补充材料可在网上查阅。
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.