提出新算法实现无维度依赖的动态定价最优损失，适合长期定价场景。
Localized exploration in contextual dynamic pricing achieves dimension-free regret
- 分三阶段：先全局探索，再局部精修，最后纯利用。
- 当时间足够长时，达到理论最优且与特征维度无关的误差上界。
- 首次建立动态定价中探索-利用权衡的数学框架，适用于各种时间长度。
研究线性需求模型下的上下文动态定价问题。提出一种新型的局部化探索-然后承诺（LetC）算法，该算法首先进行纯探索阶段，随后进入精修阶段，在已学习的最优定价策略附近进行局部探索，最后进入纯利用阶段。证明当时间跨度超过特征维度的多项式时，该算法可实现最小最大意义下、与维度无关的最优后悔上界。此外，构建了一个涵盖整个时间范围的通用理论框架，展示了在有限时间下如何平衡探索与利用。分析基于一个新颖的关键不等式，刻画了动态定价中的探索-利用权衡，类比于正则化回归中的偏差-方差权衡。理论结果通过合成数据和真实世界数据的大量实验得到验证。
原文摘要 · Abstract (English)
We study the problem of contextual dynamic pricing with a linear demand model. We propose a novel localized exploration-then-commit (LetC) algorithm which starts with a pure exploration stage, followed by a refinement stage that explores near the learned optimal pricing policy, and finally enters a pure exploitation stage. The algorithm is shown to achieve a minimax optimal, dimension-free regret bound when the time horizon exceeds a polynomial of the covariate dimension. Furthermore, we provide a general theoretical framework that encompasses the entire time spectrum, demonstrating how to balance exploration and exploitation when the horizon is limited. The analysis is powered by a novel critical inequality that depicts the exploration-exploitation trade-off in dynamic pricing, mirroring its existing counterpart for the bias-variance trade-off in regularized regression. Our theoretical results are validated by extensive experiments on synthetic and real-world data.
Thank you to arXiv for use of its open access interoperability. PaperDance 不是 arXiv 官方产品；中文卡片由大模型生成，请以原文为准。