# Learning an Optimal Assortment Policy under Observational Data

arXiv: https://arxiv.org/abs/2502.06777 · HTML: https://mlsanity.com/paper/2502.06777/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Builds on 25 of its 52 references that are in the map.
- First posted on arXiv 10 Feb 2025.

## Builds on (most cited first, 25 of 25)

- [Conservative Q-Learning for Offline Reinforcement Learning](https://mlsanity.com/paper/2006.04779/) (2020)
- [MOPO: Model-based Offline Policy Optimization](https://mlsanity.com/paper/2005.13239/) (2020)
- [Is Pessimism Provably Efficient for Offline RL?](https://mlsanity.com/paper/2012.15085/) (2020)
- [Bridging Offline Reinforcement Learning and Imitation Learning: A Tale of Pessimism](https://mlsanity.com/paper/2103.12021/) (2021)
- [Bellman-consistent Pessimism for Offline Reinforcement Learning](https://mlsanity.com/paper/2106.06926/) (2021)
- [Pessimistic Model-based Offline Reinforcement Learning under Partial Coverage](https://mlsanity.com/paper/2107.06226/) (2021)
- [Offline Reinforcement Learning with Realizability and Single-policy Concentrability](https://mlsanity.com/paper/2202.04634/) (2022)
- [Pessimistic Q-Learning for Offline Reinforcement Learning: Towards Optimal Sample Complexity](https://mlsanity.com/paper/2202.13890/) (2022)
- [Nearly Minimax Optimal Offline Reinforcement Learning with Linear Function Approximation: Single-Agent MDP and Markov Game](https://mlsanity.com/paper/2205.15512/) (2022)
- [Double Pessimism is Provably Efficient for Distributionally Robust Offline Reinforcement Learning: Generic Algorithm and Robust Partial Coverage](https://mlsanity.com/paper/2305.09659/) (2023)
- [MNL-Bandit: A Dynamic Learning Approach to Assortment Selection](https://mlsanity.com/paper/1706.03880/) (2017)
- [Pessimistic Minimax Value Iteration: Provably Efficient Equilibrium Learning from Offline Datasets](https://mlsanity.com/paper/2202.07511/) (2022)
- [Thompson Sampling for the MNL-Bandit](https://mlsanity.com/paper/1706.00977/) (2017)
- [Optimal Conservative Offline RL with General Function Approximation via Augmented Lagrangian](https://mlsanity.com/paper/2211.00716/) (2022)
- [Pessimism in the Face of Confounders: Provably Efficient Offline Reinforcement Learning in Partially Observable Markov Decision Processes](https://mlsanity.com/paper/2205.13589/) (2022)
- [Active Ranking with Subset-wise Preferences](https://mlsanity.com/paper/1810.10321/) (2018)
- [Multinomial Logit Contextual Bandits: Provable Optimality and Practicality](https://mlsanity.com/paper/2103.13929/) (2021)
- [Dynamic pricing and assortment under a contextual MNL demand](https://mlsanity.com/paper/2110.10018/) (2021)
- [Nearly Minimax Optimal Regret for Multinomial Logistic Bandit](https://mlsanity.com/paper/2405.09831/) (2024)
- [Multinomial Logit Bandit with Linear Utility Functions](https://mlsanity.com/paper/1805.02971/) (2018)
- [Assortment Optimization under Unknown MultiNomial Logit Choice Models](https://mlsanity.com/paper/1704.00108/) (2017)
- [Stop Relying on No-Choice and Do not Repeat the Moves: Optimal, Efficient and Practical Algorithms for Assortment Optimization](https://mlsanity.com/paper/2402.18917/) (2024)
- [PASTA: Pessimistic Assortment Optimization](https://mlsanity.com/paper/2302.03821/) (2023)
- [MNL-Bandit with Knapsacks: a near-optimal algorithm](https://mlsanity.com/paper/2106.01135/) (2021)
- [A Re-solving Heuristic for Dynamic Assortment Optimization with Knapsack Constraints](https://mlsanity.com/paper/2407.05564/) (2024)

## Built on by (most cited first, 4 of 4)

- [PASTA: A Unified Framework for Offline Assortment Learning](https://mlsanity.com/paper/2510.01693/) (2025)
- [Optimal Exploration of New Products under Assortment Decisions](https://mlsanity.com/paper/2604.18800/) (2026)
- [Learning in Position-Aware Multinomial Logit Bandits: From Multiplicative to General Position Effects](https://mlsanity.com/paper/2605.17238/) (2026)
- [Diffusion-Based Data-Driven Assortment Optimization](https://mlsanity.com/paper/2608.11419/) (2026)

## Abstract (arXiv)

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.