面向始终有效的高维动态定价的在线正则化
Online Regularization towards Always-Valid High-Dimensional Dynamic Pricing
AI总结：
针对动态定价中在线不确定性适应受限的问题，提出基于在线正则化的乐观在线正则化极大似然定价（OORMLP）算法，利用非渐近鞅集中度实现始终有效的高维定价，理论确保对数遗憾，实验证明其优于现有方法。
摘要：
设计具有始终有效的在线统计学习程序的动态定价策略是一个重要且尚未解决的问题。大多数现有的动态定价策略侧重于所采用的客户选择模型的忠实度，在定价过程中对学习到的统计模型的在线不确定性表现出有限的适应能力。在本文中，我们提出了一种基于正则化在线统计学习并具有理论保证的设计动态定价策略的新方法。该新方法克服了对在线Lasso过程进行连续监测的挑战，并具有几个吸引人的特性。特别是，我们做出了决定性的观察，即定价决策的始终有效性建立并依赖于在线正则化方案。我们提出的在线正则化方案赋予了所提出的乐观在线正则化极大似然定价（OORMLP）定价策略三个主要优势：将市场噪声知识编码到定价过程的乐观性中；在所有决策点上赋予在线统计学习始终有效性；用时间一致的非渐近预言机不等式包络预测误差过程。这类非渐近推断结果使我们能够在实践中设计更具样本效率和鲁棒性的动态定价算法。在理论上，所提出的OORMLP算法利用了高维模型的稀疏结构，并在决策视界内确保了对数遗憾。这些理论进展是通过提出一种乐观的在线Lasso过程实现的，该过程基于非渐近鞅集中度的新颖应用，在过程层面解决了动态定价问题。在实验中，我们在不同的合成和实际定价问题设置中评估了OORMLP，并证明OORMLP超越了现有最先进的方法。
英文摘要：
Devising dynamic pricing policy with always valid online statistical learning procedure is an important and as yet unresolved problem. Most existing dynamic pricing policy, which focus on the faithfulness of adopted customer choice models, exhibit a limited capability for adapting the online uncertainty of learned statistical model during pricing process. In this paper, we propose a novel approach for designing dynamic pricing policy based regularized online statistical learning with theoretical guarantees. The new approach overcomes the challenge of continuous monitoring of 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 over all decision points; envelop 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.
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