# Dynamic Assortment Optimization with Changing Contextual Information

arXiv: https://arxiv.org/abs/1810.13069 · HTML: https://mlsanity.com/paper/1810.13069/

## Key facts

- Cited by 28 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 31 Oct 2018.

## Built on by (most cited first, 28 of 28)

- [Reinforcement Learning with Human Feedback: Learning Dynamic Choices via Pessimism](https://mlsanity.com/paper/2305.18438/) (2023)
- [Optimization with Constraint Learning: A Framework and Survey](https://mlsanity.com/paper/2110.02121/) (2021)
- [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)
- [Improved Online Confidence Bounds for Multinomial Logistic Bandits](https://mlsanity.com/paper/2502.10020/) (2025)
- [UCB-based Algorithms for Multinomial Logistic Regression Bandits](https://mlsanity.com/paper/2103.11489/) (2021)
- [Testing Stationarity and Change Point Detection in Reinforcement Learning](https://mlsanity.com/paper/2203.01707/) (2022)
- [Spectral Ranking Inferences based on General Multiway Comparisons](https://mlsanity.com/paper/2308.02918/) (2023)
- [Doubly High-Dimensional Contextual Bandits: An Interpretable Model for Joint Assortment-Pricing](https://mlsanity.com/paper/2309.08634/) (2023)
- [Contextual Online Uncertainty-Aware Preference Learning for Human Feedback](https://mlsanity.com/paper/2504.19342/) (2025)
- [Structured Reinforcement Learning for Combinatorial Decision-Making](https://mlsanity.com/paper/2505.19053/) (2025)
- [Contextual Multinomial Logit Bandits with General Value Functions](https://mlsanity.com/paper/2402.08126/) (2024)
- [Generalized Low-Rank Matrix Contextual Bandits with Graph Information](https://mlsanity.com/paper/2507.17528/) (2025)
- [Doubly Inhomogeneous Reinforcement Learning](https://mlsanity.com/paper/2211.03983/) (2022)
- [PASTA: Pessimistic Assortment Optimization](https://mlsanity.com/paper/2302.03821/) (2023)
- [Low-Rank Online Dynamic Assortment with Dual Contextual Information](https://mlsanity.com/paper/2404.17592/) (2024)
- [PASTA: A Unified Framework for Offline Assortment Learning](https://mlsanity.com/paper/2510.01693/) (2025)
- [Preference-based Reinforcement Learning beyond Pairwise Comparisons: Benefits of Multiple Options](https://mlsanity.com/paper/2510.18713/) (2025)
- [Pure Exploration with Structured Preference Feedback](https://mlsanity.com/paper/2104.05294/) (2021)
- [Combinatorial Inference on the Optimal Assortment in Multinomial Logit Models](https://mlsanity.com/paper/2301.12254/) (2023)
- [Online Joint Assortment-Inventory Optimization under MNL Choices](https://mlsanity.com/paper/2304.02022/) (2023)
- [A Re-solving Heuristic for Dynamic Assortment Optimization with Knapsack Constraints](https://mlsanity.com/paper/2407.05564/) (2024)
- [Differentiable Knapsack and Top-k Operators via Dynamic Programming](https://mlsanity.com/paper/2601.21775/) (2026)
- [Offline Clustering of Preference Learning with Active-data Augmentation](https://mlsanity.com/paper/2510.26301/) (2025)
- [Tractable Multinomial Logit Contextual Bandits with Non-Linear Utilities](https://mlsanity.com/paper/2601.06913/) (2026)
- [Optimal Design for Multinomial Logit Model with Applications to Best Assortment Identification](https://mlsanity.com/paper/2605.25592/) (2026)
- [Diversified Multinomial Logit Contextual Bandits](https://mlsanity.com/paper/2607.11684/) (2026)

## Abstract (arXiv)

In this paper, we study the dynamic assortment optimization problem under a finite selling season of length T. At each time period, the seller offers an arriving customer an assortment of substitutable products under a cardinality constraint, and the customer makes the purchase among offered products according to a discrete choice model. Most existing work associates each product with a real-valued fixed mean utility and assumes a multinomial logit choice (MNL) model. In many practical applications, feature/contexutal information of products is readily available. In this paper, we incorporate the feature information by assuming a linear relationship between the mean utility and the feature. In addition, we allow the feature information of products to change over time so that the underlying choice model can also be non-stationary. To solve the dynamic assortment optimization under this changing contextual MNL model, we need to simultaneously learn the underlying unknown coefficient and makes the decision on the assortment. To this end, we develop an upper confidence bound (UCB) based policy and establish the regret bound on the order of widetilde O(d√T), where d is the dimension of the feature and widetilde O suppresses logarithmic dependence. We further established the lower bound Omega(d√T/K) where K is the cardinality constraint of an offered assortment, which is usually small. When K is a constant, our policy is optimal up to logarithmic factors. In the exploitation phase of the UCB algorithm, we need to solve a combinatorial optimization for assortment optimization based on the learned information. We further develop an approximation algorithm and an efficient greedy heuristic. The effectiveness of the proposed policy is further demonstrated by our numerical studies.