Learning an Optimal Assortment Policy under Observational Data

TL;DR

This paper investigates the minimal data needed for offline assortment optimization under the MNL model, introducing a nearly optimal algorithm that relaxes previous data requirements and provides fundamental insights into offline learning.

Contribution

The paper proposes Pessimistic Rank-Breaking, an algorithm that achieves near minimax optimality and relaxes data requirements for offline assortment optimization under the MNL model.

Findings

PRB algorithm is nearly minimax optimal.

Optimal item coverage is necessary and sufficient for efficient offline learning.

Relaxed data requirements compared to previous methods.

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.