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arXiv 2012.03800cs.LG
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产品排序中的收益最大化与学习

Revenue Maximization and Learning in Products Ranking

Ningyuan Chen, Anran Li, Shuoguang Yang

AI总结:

本文研究在线零售商在消费者注意力跨度随机且未知条件下的产品排序收益最大化问题,提出具有嵌套结构的最优排序近似算法,并设计在线学习算法实现次线性遗憾。

摘要:

我们考虑一个在线零售商的收益最大化问题,该零售商计划按顺序展示一组在价格和质量上有所不同的产品。消费者具有注意力跨度,即他们愿意查看的最大产品数量,并依次检查产品,然后购买某个产品或在其注意力跨度耗尽时空手离开平台。我们的框架在两个方向上扩展了众所周知的级联模型:消费者具有随机的注意力跨度而非固定的注意力跨度,并且企业最大化收益而非点击概率。我们证明了当注意力跨度固定时,最优产品排序作为注意力跨度的函数具有嵌套结构。利用这一事实,当仅给出注意力跨度的分布时,我们开发了一种近似算法。在温和条件下,当已实现的注意力跨度已知时,该算法能达到透视情形收益的$1/e$。我们还证明,没有任何算法能达到同一基准收益的0.5以上。该模型和算法可以推广到消费者进行多次购买时的排序问题。当条件购买概率未知且可能依赖于消费者和产品特征时,我们设计了一种在线学习算法,尽管存在信息删失——购买商品的顾客的注意力跨度不可观测——该算法仍能实现相对于近似算法的$\tilde{\mathcal{O}}(\sqrt{T})$遗憾。数值实验证明了近似算法和在线学习算法的出色性能。

英文摘要:

We consider the revenue maximization problem for an online retailer who plans to display in order a set of products differing in their prices and qualities. Consumers have attention spans, i.e., the maximum number of products they are willing to view, and inspect the products sequentially before purchasing a product or leaving the platform empty-handed when the attention span gets exhausted. Our framework extends the well-known cascade model in two directions: the consumers have random attention spans instead of fixed ones, and the firm maximizes revenues instead of clicking probabilities. We show a nested structure of the optimal product ranking as a function of the attention span when the attention span is fixed. \sg{Using this fact, we develop an approximation algorithm when only the distribution of the attention spans is given. Under mild conditions, it achieves $1/e$ of the revenue of the clairvoyant case when the realized attention span is known. We also show that no algorithms can achieve more than 0.5 of the revenue of the same benchmark. The model and the algorithm can be generalized to the ranking problem when consumers make multiple purchases.} When the conditional purchase probabilities are not known and may depend on consumer and product features, we devise an online learning algorithm that achieves $\tilde{\mathcal{O}}(\sqrt{T})$ regret relative to the approximation algorithm, despite the censoring of information: the attention span of a customer who purchases an item is not observable. Numerical experiments demonstrate the outstanding performance of the approximation and online learning algorithms.

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

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