arXiv:2602.10696stat.MLcs.LG2026-02

在用户偏好变化时仍能保证收益,提升推荐系统稳定性。

Robust Assortment Optimization from Observational Data

  • 构建对抗分布偏移的鲁棒优化框架,最大化最差情况下的预期收益。
  • 理论证明需至少满足‘鲁棒项覆盖’才能实现高效学习,样本复杂度有上下界。
  • 适合追求高可靠性、抗数据漂移的电商与推荐系统开发者。

组合优化是现代零售与推荐系统的核心挑战,目标是在复杂的用户选择行为下,选出能最大化预期收入的产品子集。尽管数据驱动方法利用历史数据进行学习与优化,但通常依赖于客户偏好稳定和选择模型正确的强假设。然而在真实场景中,偏好转移和模型误设常导致泛化能力差与收益损失。为此,我们提出一种鲁棒的数据驱动组合优化框架,考虑客户选择行为的潜在分布偏移。该方法以生成数据的名义选择模型为基础,寻求最坏情况下的最大预期收益。我们首先证明当名义模型已知时,鲁棒组合规划具有计算可解性;进而推进到数据驱动设置,设计出统计最优算法,在保持鲁棒性的同时最小化数据需求。理论分析给出了样本复杂度的上下界,提供鲁棒泛化的理论保障。特别地,我们揭示并定义了‘鲁棒项覆盖’为实现样本高效鲁棒组合学习的最小数据要求。本工作弥合了鲁棒性与统计效率之间的鸿沟,为不确定性下的可靠组合优化提供了新见解与工具。

原文摘要 · Abstract (English)

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.

组合优化鲁棒学习推荐系统

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