Online Regularization toward Always-Valid High-Dimensional Dynamic Pricing
面向始终有效高维动态定价的在线正则化AI 解读 ↓
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面向始终有效高维动态定价的在线正则化
- 研究问题
- 如何在高维动态定价过程中持续监测在线模型的不确定性，使定价学习在各决策时点保持有效并控制累计遗憾？
- 方法与思路
- 作者提出乐观在线正则化极大似然定价策略，以在线 Lasso 正则化和非渐近鞅集中分析构造时间一致误差控制。
- 材料陈述的贡献
- 摘要称获得覆盖各决策时点的有效性与时间一致预言不等式，并利用稀疏结构证明决策期限上的对数级遗憾。
- 阅读关注点
- 应核对客户选择与需求模型、市场噪声信息的使用、在线正则化设置，以及时间一致保证和对数遗憾成立的条件。
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原文摘要
–Devising a dynamic pricing policy with always valid online statistical learning procedures is an important and as yet unresolved problem. Most existing dynamic pricing policies, which focus on the faithfulness of adopted customer choice models, exhibit a limited capability for adapting to the online uncertainty of learned statistical models during the pricing process. In this article, we propose a novel approach for designing a dynamic pricing policy based on regularized online statistical learning with theoretical guarantees. The new approach overcomes the challenge of continuous monitoring of the online Lasso procedure and possesses several appealing properties. In particular, we make the decisive observation that the always-validity of pricing decisions builds and thrives on the online regularization scheme. Our proposed online regularization scheme equips the proposed optimistic online regularized maximum likelihood pricing (OORMLP) pricing policy with three major advantages: encode market noise knowledge into pricing process optimism; empower online statistical learning with always-validity overall decision points; envelope prediction error process with time-uniform non-asymptotic oracle inequalities. This type of non-asymptotic inference results allows us to design more sample-efficient and robust dynamic pricing algorithms in practice. In theory, the proposed OORMLP algorithm exploits the sparsity structure of high-dimensional models and secures a logarithmic regret in a decision horizon. These theoretical advances are made possible by proposing an optimistic online Lasso procedure that resolves dynamic pricing problems at the process level, based on a novel use of non-asymptotic martingale concentration. In experiments, we evaluate OORMLP in different synthetic and real pricing problem settings and demonstrate that OORMLP advances the state-of-the-art methods. Supplementary materials for this article are available online.