论文标题

产品排名的收入最大化和学习

Revenue Maximization and Learning in Products Ranking

论文作者

Chen, Ningyuan, Li, Anran, Yang, Shuoguang

论文摘要

我们考虑了一家计划展示的在线零售商的收入最大化问题,以使其价格和质量不同。消费者的注意力跨度,即,他们愿意查看的最大产品数量,并在购买产品或在注意力范围耗尽时依次检查产品。我们的框架将众所周知的级联模型扩展到两个方向上:消费者具有随机的注意力跨度,而不是固定的,而公司可以最大化收入而不是单击概率。当固定注意力跨度时,我们显示了最佳产品排名的嵌套结构。 \ sg {使用这个事实,我们开发了一个近似算法时,只有给出注意力跨度的分布。在温和的条件下,当已知的注意力跨度已知时,它可以达到千里市场的收入$ 1/e $。我们还表明,没有算法可以达到同一基准收入的0.5以上。当消费者进行多次购买时,该模型和算法可以推广到排名问题。}当有条件购买概率不知道并且可能取决于消费者和产品功能时,我们设计了一种在线学习算法,该算法达到$ \ tilde {\ tilde {\ natercal {\ natercal {o}}}}(O}}}(\ sqrth and tosim,信息:购买商品的客户的注意力跨度无法观察到。数值实验证明了近似和在线学习算法的出色性能。

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.

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