[论文解读] A Solicit-Then-Suggest Model of Agentic Purchasing

Shengyu Cao, Ming Hu|arXiv (Cornell University)|Mar 21, 2026

Auction Theory and Applications被引用 0

一句话总结

本文将一个AI购物代理的流程形式化为先通过多轮提问了解客户偏好，再提供一个小而定制的商品集合；征询深度和商品集合的广度是以不同效率的替代品。

ABSTRACT

E-commerce is shifting from search-based shopping to agentic purchasing. Rather than relying on keywords, AI shopping agents learn customer preferences through targeted multi-round conversations and then recommend a tailored set of products. We develop a solicit-then-suggest framework to study this setting. In a d-dimensional preference space, an agent conducts m rounds of solicitation to refine its belief about the customer's ideal product, then recommends k products from which the customer chooses. Our analysis identifies the key economic tradeoff. Under a Gaussian prior, we establish an uncertainty decomposition: solicitation depth and assortment breadth are substitutes, with total prior uncertainty split between what solicitation resolves and what assortment breadth hedges. The two instruments improve match quality at very different rates. Expected loss decreases on the order of 1/m with solicitation depth, but only on the order of k^(-2/d) with assortment breadth, reflecting a curse of dimensionality. Thus, a few well-designed questions can achieve what would otherwise require far more recommendations. We also characterize the optimal policy. The optimal assortment forms a Voronoi partition, assigning each product to the posterior region it best serves. With a single recommended product, the optimal solicitation follows a water-filling rule that equalizes posterior uncertainty across dimensions. With multiple products, the optimum may allocate less precision to dimensions that the assortment can hedge. This single-product water-filling rule also yields a general approximation guarantee for larger assortments, and the gap vanishes as dimension grows. Beyond the Gaussian case, the uncertainty decomposition and substitutability between solicitation depth and assortment breadth continue to hold for non-Gaussian priors.

研究动机与目标

• 将代理式购买定义为相较于传统搜索的一种偏好获取的新范式，通过对话实现多轮偏好获取。
• Develop a tractable probabilistic model (solicit-then-suggest) that jointly optimizes information gathering and downstream assortment design.
• Characterize how solicitation depth and assortment breadth interact, including their substitution relationship and effect on match quality.
• Provide optimal policies for single- and multi-product assortments under Gaussian priors, and extend results to non-Gaussian priors.
• Offer design guidance for practical systems, including when a simple single-question policy suffices for larger assortments.

提出的方法

• 将客户建模为在 d 维空间中的潜在理想点 θ，先验为高斯分布 N(μ0, Σ0)。
• 使用 m 轮方向性询问，单位范数 y_t，噪声响应 z_t = θᵀy_t + ε_t，通过卡尔曼滤波方程（κ_t, μ_t, Σ_t）更新信念。
• 在经过 m 轮后，选择 k 个产品形成Voronoi分区的最优集合，将每个产品放置在其区域的后验质心处。
• 证明当 k=1 时，最优推荐是后验均值，期望损失等于后验方差的一半。
• 为单产品情形推导水位填充的征询策略，并在扩展到较大集合时给出效率差距界。
• 在高斯先验之外扩展分析，建立不确定性分解恒等式以及征询与集合广度之间的可替代性。

实验结果

研究问题

• RQ1 代理式购买中征询深度与商品集合广度如何相互作用？
• RQ2 在高斯先验下，选择查询方向和商品集合的最优策略是什么？
• RQ3 随着提问增多与产品增多，期望损失降低的速率为何不同？
• RQ4 核心结果是否可以推广到非高斯先验，且高斯基准在渐近情况的表现如何？
• RQ5 信息收集与产品对冲之间的相互作用会给出哪些实际设计指导？

主要发现

• 不确定性可分解性：总先验不确定性分成被征询消除的部分和定制化商品对冲的部分；征询与集合是可替代的。
• 在征询深度下，期望损失以 O(1/m) 下降；而对包含 k 个产品的集合，损失以 O(k^{-2/d}) 下降，显示广度存在维度灾难，但对查询不。
• 单产品最优集合将产品放在后验均值处，损失等于后验方差的一半；多产品集合形成Voronoi分区，产品位于后验质心。
• 水位填充征询策略使主动学习的维度后验不确定性趋于均衡，在小 m 与较大 d 时接近最优；在联合优化中可能出现选择性聚焦。
• 高斯结果为非高斯先验提供保守基准，随着对话长度增长在渐近意义上达到精确性。