基于历史数据，高效学习最优商品组合策略。
Learning an Optimal Assortment Policy under Observational Data
- 提出悲观排序分解算法，结合排序拆分与保守估计。
- 证明算法近乎最优，仅需每件商品在数据中充分出现即可。
- 适用于无法频繁试错的真实商业场景，如电商选品。
我们研究在多项式逻辑（MNL）模型下，仅基于历史客户选择数据进行离线商品组合优化的基本问题。现有方法多依赖与客户反复互动的在线学习，但在许多现实场景中探索成本过高或不可行。本文采用离线学习范式，探究高效离线优化所需的最小数据量。为此，提出悲观排序分解（PRB）算法，融合排序拆分与悲观估计。证明了PRB近乎极小极大最优：建立了紧致的次优性上界，并给出几乎匹配的下界。结果表明，'最优商品覆盖率'——即最优组合中的每件商品在历史数据中出现足够频繁——既是高效离线学习的充分条件，也是必要条件。这显著放宽了以往必须完整观测到最优组合的严苛要求。研究为MNL模型下的离线组合优化提供了根本性的数据需求洞见。
原文摘要 · Abstract (English)
We study the fundamental problem of offline assortment optimization under the Multinomial Logit (MNL) model, where sellers must determine the optimal subset of the products to offer based solely on historical customer choice data. While most existing approaches to learning-based assortment optimization focus on the online learning of the optimal assortment through repeated interactions with customers, such exploration can be costly or even impractical in many real-world settings. In this paper, we consider the offline learning paradigm and investigate the minimal data requirements for efficient offline assortment optimization. To this end, we introduce Pessimistic Rank-Breaking (PRB), an algorithm that combines rank-breaking with pessimistic estimation. We prove that PRB is nearly minimax optimal by establishing the tight suboptimality upper bound and a nearly matching lower bound. This further shows that "optimal item coverage" - where each item in the optimal assortment appears sufficiently often in the historical data - is both sufficient and necessary for efficient offline learning. This significantly relaxes the previous requirement of observing the complete optimal assortment in the data. Our results provide fundamental insights into the data requirements for offline assortment optimization under the MNL model.
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