基于历史数据优化商品组合,用悲观原则提升收益可靠性。
PASTA: A Unified Framework for Offline Assortment Learning
- 采用悲观策略,在数据不全时仍能保证最优收益。
- 首次建立多类选择模型的有限样本误差边界,理论更完善。
- 适合缺乏完整数据的电商场景,尤其适合新平台冷启动。
我们研究一类离线、数据驱动的组合优化问题。企业在不了解顾客选择行为的前提下,需根据历史选择数据确定最优商品组合。由于组合数量庞大,常导致数据覆盖不足,难以设计出有保障效果的方法。为此,我们提出一种新的悲观组合优化(PASTA)框架,利用悲观原则,在一般选择模型下实现最优期望收益。关键优势在于:仅需离线数据包含一个最优组合,无需覆盖所有可能组合。理论上,我们首次为多种常用选择模型(如多项对数和嵌套对数模型)建立了有限样本后悔边界,并推导了极小极大后悔下界,证明PASTA在样本与模型复杂度上均达到最优。数值实验表明,该方法优于现有基准方法。
原文摘要 · Abstract (English)
We study a broad class of assortment optimization problems in an offline and data-driven setting. In such problems, a firm lacks prior knowledge of the underlying choice model, and aims to determine an optimal assortment based on historical customer choice data. The combinatorial nature of assortment optimization often results in insufficient data coverage, posing a significant challenge in designing provably effective solutions. To address this, we introduce a novel Pessimistic Assortment Optimization (PASTA) framework that leverages the principle of pessimism to achieve optimal expected revenue under general choice models. Notably, PASTA requires only that the offline data distribution contains an optimal assortment, rather than providing the full coverage of all feasible assortments. Theoretically, we establish the first finite-sample regret bounds for offline assortment optimization across several widely used choice models, including the multinomial logit and nested logit models. Additionally, we derive a minimax regret lower bound, proving that PASTA is minimax optimal in terms of sample and model complexity. Numerical experiments further demonstrate that our method outperforms existing baseline approaches.
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