arXivDaily arXiv每日学术速递 周一至周五更新
arXiv 2011.10690cs.LGcs.IR
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需求学习中的自适应风险缓解

Adaptive Risk Mitigation in Demand Learning

University of Michigan(密歇根大学)

Parshan Pakiman, Boxiao Chen, Selvaprabu Nadarajah, Stefanus Jasin

AI总结:

本文提出自适应风险学习框架,通过动态调整模糊集来平衡需求学习中的风险与遗憾,实现高收入和低风险。

摘要:

我们研究了一个具有未知需求分布的产品在有限时间 horizon 内的动态定价问题。不同于标准无遗憾学习环境,其中价格可以在任何时间调整,我们限制价格变化到预定的时间点,以反映常见的零售实践。这一约束,加上需求模型的模糊性和未知的顾客到达模式,导致了高收入损失的风险,因为基于错误估计的需求模型的价格可能被应用于许多顾客,直到其可以被修订。我们开发了一个自适应风险学习(ARL)框架,该框架嵌入了一个数据驱动的模糊集(DAS),通过适应于未知的到达模式来量化需求模型的模糊性。最初,当到达较少时,DAS包括一个广泛的可能需求模型集,反映出高模糊性和收入风险。随着通过定价收集的新数据,DAS逐步缩小,捕捉到模型模糊性和相关风险的减少。我们建立了DAS概率收敛到真实需求模型的性质,并推导了ARL策略的遗憾界,该界明确将收入损失与DAS识别真实模型所需的数据联系起来。我们的遗憾界对到达模式的依赖是独一无二的,与无遗憾学习环境不同,其中遗憾是常数且与到达模式无关。放松对不频繁价格变化的约束,我们证明ARL达到已知的常数遗憾界。数值实验进一步表明,ARL在优先考虑遗憾或风险的基准上表现更优,通过自适应平衡两者,而无需了解到达模式。这种自适应风险调整对于在价格粘性且需求和到达模式未知的情况下实现高收入和低下行风险至关重要。

英文摘要:

We study dynamic pricing of a product with an unknown demand distribution over a finite horizon. Departing from the standard no-regret learning environment in which prices can be adjusted at any time, we restrict price changes to predetermined points in time to reflect common retail practice. This constraint, coupled with demand model ambiguity and an unknown customer arrival pattern, imposes a high risk of revenue loss, as a price based on a misestimated demand model may be applied to many customers before it can be revised. We develop an adaptive risk learning (ARL) framework that embeds a data-driven ambiguity set (DAS) to quantify demand model ambiguity by adapting to the unknown arrival pattern. Initially, when arrivals are few, the DAS includes a broad set of plausible demand models, reflecting high ambiguity and revenue risk. As new data is collected through pricing, the DAS progressively shrinks, capturing the reduction in model ambiguity and associated risk. We establish the probabilistic convergence of the DAS to the true demand model and derive a regret bound for the ARL policy that explicitly links revenue loss to the data required for the DAS to identify the true model with high probability. The dependence of our regret bound on the arrival pattern is unique to our constrained dynamic pricing problem and contrasts with no-regret learning environments, where regret is constant and arrival-pattern independent. Relaxing the constraint on infrequent price changes, we show that ARL attains the known constant regret bound. Numerical experiments further demonstrate that ARL outperforms benchmarks that prioritize either regret or risk alone by adaptively balancing both without knowledge of the arrival pattern. This adaptive risk adjustment is crucial for achieving high revenues and low downside risk when prices are sticky and both demand and arrival patterns are unknown.

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