发表机构
School of Management, Fudan University; Mendoza College of Business, University of Notre Dame（复旦大学管理学院; 圣母大学门多萨商学院）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
研究非平稳下的上下文动态定价问题，提出基于多尺度变化点检测的自适应算法，能在不知分段平稳段数量和模型参数设计调整变化预算时实现最优收益，填补文献空白，经实验验证算法效率和鲁棒性。
AI 中文摘要
我们研究非平稳情况下的上下文动态定价问题，企业向T个依次到来的消费者销售产品，消费者行为依未知且随时间变化的需求模型。需求模型假设为广义线性模型（GLM），有特征向量编码产品和消费者信息。为实现最优收益（即最小遗憾值），企业需学习并利用未知GLM同时监测潜在变化。我们提出基于多尺度变化点检测的算法，其遗憾值为$\widetilde{O}(\sqrt{s_TdT}\wedge\{V_T^{1/3}d^{1/3}T^{2/3}+\sqrt{dT}\})$（$s_T$为分段平稳段数量，$V_T$为新定义的模型参数设计调整变化预算概念）。该算法自适应，无需知道$s_T$或$V_T$。这是首个适应变化本质且达到两全其美速率的动态定价算法，填补文献长期空白。现有自适应非平稳博弈文献工作因上下文变化无法用于实现上下文动态定价最优性。遗憾值还有新构建的极小极大下界，证实算法最优性（至多对数因子）。进行大量数值实验说明算法在非平稳动态定价中的效率和鲁棒性。
英文摘要
We study the contextual dynamic pricing problem under non-stationarity, where a firm sells products to $T$ sequentially arriving consumers that behave according to an unknown demand model that can change over time. The demand model is assumed to be a generalized linear model (GLM), allowing for a feature vector in $\mathbb{R}^d$ that encodes products and consumer information. To achieve optimal revenue (i.e., least regret), the firm needs to learn and exploit the unknown GLMs while monitoring for potential changes. We propose a multiscale change-point detection based algorithm that achieves a regret of order $\widetilde{O}(\sqrt{s_TdT}\wedge\{V_T^{1/3}d^{1/3}T^{2/3}+\sqrt{dT}\})$, where $s_T$ is the number of piecewise stationary segments and $V_T$ is a newly defined notion of design-adjusted variation budget of model parameters. Our algorithm is adaptive and does not require knowing $s_T$ or $V_T$. Moreover, to our knowledge, this is the first dynamic pricing algorithm that is adaptive to the nature of changes and achieves the best-of-both-worlds rate, thus closing a long-standing gap in the literature. We remark that, due to the varying contexts, existing works in the adaptive non-stationary bandit literature cannot be applied to achieve optimality for contextual dynamic pricing. The regret is further accompanied with a newly constructed minimax lower bound, confirming the optimality of our algorithm (up to logarithmic factors). Extensive numerical experiments are conducted to illustrate the efficiency and robustness of the proposed algorithm in non-stationary dynamic pricing.
