Learning an Optimal Assortment Policy under Observational Data

2025-02-10

AI Summary

This paper studies offline assortment optimization under the Multinomial Logit (MNL) model using only historical customer choice data, aiming to identify the optimal subset of products. We propose the Pessimistic Ranking-Based (PRB) algorithm, which—uniquely—characterizes offline learnability via the necessary and sufficient condition of “optimal product coverage,” a significantly weaker requirement than prior assumptions demanding full observation of the optimal assortment. PRB integrates ranking-based decomposition with pessimistic estimation and derives tight upper and lower bounds on suboptimality through minimax analysis. Theoretically, PRB is shown to be nearly minimax-optimal, revealing the fundamental data requirements for efficient offline learning and providing a practical, verifiable coverage criterion for implementation.

Technology Category

• Machine Learning: Learning Preferences or Rankings
• Search and Optimization: Learning to Search
• Reasoning under Uncertainty: Stochastic Optimization

Application Category

• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• User Modeling, Personalization and Recommendation: Fairness-aware retrieval and ranking
• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs

Abstract

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.

Problem

• Offline assortment optimization under MNL model
• Minimal data requirements for efficient learning
• Optimal item coverage in historical data

Innovation

• Offline assortment optimization
• Pessimistic Rank-Breaking algorithm
• Optimal item coverage requirement