Assortment optimization is a fundamental challenge in modern retail and recommendation systems, where the goal is to select a subset of products that maximizes expected revenue under complex customer choice behaviors. While recent advances in data-driven methods have leveraged historical data to learn and optimize assortments, these approaches typically rely on strong assumptions -- namely, the stability of customer preferences and the correctness of the underlying choice models. However, such assumptions frequently break in real-world scenarios due to preference shifts and model misspecification, leading to poor generalization and revenue loss. Motivated by this limitation, we propose a robust framework for data-driven assortment optimization that accounts for potential distributional shifts in customer choice behavior. Our approach models potential preference shift from a nominal choice model that generates data and seeks to maximize worst-case expected revenue. We first establish the computational tractability of robust assortment planning when the nominal model is known, then advance to the data-driven setting, where we design statistically optimal algorithms that minimize the data requirements while maintaining robustness. Our theoretical analysis provides both upper bounds and matching lower bounds on the sample complexity, offering theoretical guarantees for robust generalization. Notably, we uncover and identify the notion of ``robust item-wise coverage'' as the minimal data requirement to enable sample-efficient robust assortment learning. Our work bridges the gap between robustness and statistical efficiency in assortment learning, contributing new insights and tools for reliable assortment optimization under uncertainty.

翻译：商品组合优化是现代零售与推荐系统中的核心挑战，其目标是在复杂的顾客选择行为下，选取能够最大化期望收益的产品子集。尽管近年来数据驱动方法利用历史数据学习并优化商品组合，但这些方法通常依赖于强假设——即顾客偏好的稳定性与底层选择模型的正确性。然而，在现实场景中，由于偏好漂移和模型设定错误，此类假设往往难以成立，导致泛化能力差和收益损失。针对这一局限，我们提出一种鲁棒的数据驱动商品组合优化框架，该框架能够应对顾客选择行为中潜在的分布漂移。我们的方法从生成数据的名义选择模型出发，建模潜在的偏好漂移，并寻求最大化最坏情况下的期望收益。我们首先证明了在名义模型已知时鲁棒商品组合规划的计算可行性，进而推进到数据驱动场景，设计了统计最优算法，在保持鲁棒性的同时最小化数据需求。我们的理论分析给出了样本复杂度的上界与匹配下界，为鲁棒泛化提供了理论保证。值得注意的是，我们提出并定义了“鲁棒逐项覆盖”的概念，将其作为实现样本高效鲁棒商品组合学习的最小数据要求。本研究弥合了商品组合学习中鲁棒性与统计效率之间的鸿沟，为不确定性下的可靠商品组合优化提供了新的见解与工具。