# MNL-Bandits under Inventory and Limited Switches Constraints

arXiv: https://arxiv.org/abs/2204.10787 · HTML: https://mlsanity.com/paper/2204.10787/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 7 of its 23 references that are in the map.
- First posted on arXiv 22 Apr 2022.

## Builds on (most cited first, 7 of 7)

- [Bandits with Knapsacks](https://mlsanity.com/paper/1305.2545/) (2013)
- [Batched Multi-armed Bandits Problem](https://mlsanity.com/paper/1904.01763/) (2019)
- [MNL-Bandit: A Dynamic Learning Approach to Assortment Selection](https://mlsanity.com/paper/1706.03880/) (2017)
- [Thompson Sampling for the MNL-Bandit](https://mlsanity.com/paper/1706.00977/) (2017)
- [Dynamic Assortment Personalization in High Dimensions](https://mlsanity.com/paper/1610.05604/) (2016)
- [Assortment Optimization under Unknown MultiNomial Logit Choice Models](https://mlsanity.com/paper/1704.00108/) (2017)
- [MNL-Bandit with Knapsacks: a near-optimal algorithm](https://mlsanity.com/paper/2106.01135/) (2021)

## Abstract (arXiv)

Optimizing the assortment of products to display to customers is a key to increasing revenue for both offline and online retailers. To trade-off between exploring customers' preference and exploiting customers' choices learned from data, in this paper, by adopting the Multi-Nomial Logit (MNL) choice model to capture customers' choices over products, we study the problem of optimizing assortments over a planning horizon T for maximizing the profit of the retailer. To make the problem setting more practical, we consider both the inventory constraint and the limited switches constraint, where the retailer cannot use up the resource inventory before time T and is forbidden to switch the assortment shown to customers too many times. Such a setting suits the case when an online retailer wants to dynamically optimize the assortment selection for a population of customers. We develop an efficient UCB-like algorithm to optimize the assortments while learning customers' choices from data. We prove that our algorithm can achieve a sub-linear regret bound tildeOleft(T1-α/2right) if O(Tα) switches are allowed. %, and our regret bound is optimal with respect to T. Extensive numerical experiments show that our algorithm outperforms baselines and the gap between our algorithm's performance and the theoretical upper bound is small.