# Robust Dynamic Assortment Optimization in the Presence of Outlier Customers

arXiv: https://arxiv.org/abs/1910.04183 · HTML: https://mlsanity.com/paper/1910.04183/

## Key facts

- Cited by 8 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 9 Oct 2019.

## Built on by (most cited first, 8 of 8)

- [Learning in Stackelberg Games with Non-myopic Agents](https://mlsanity.com/paper/2208.09407/) (2022)
- [Doubly High-Dimensional Contextual Bandits: An Interpretable Model for Joint Assortment-Pricing](https://mlsanity.com/paper/2309.08634/) (2023)
- [Best of Many Worlds Guarantees for Online Learning with Knapsacks](https://mlsanity.com/paper/2202.13710/) (2022)
- [Density-Based Algorithms for Corruption-Robust Contextual Search and Convex Optimization](https://mlsanity.com/paper/2206.07528/) (2022)
- [Low-Rank Online Dynamic Assortment with Dual Contextual Information](https://mlsanity.com/paper/2404.17592/) (2024)
- [Combinatorial Inference on the Optimal Assortment in Multinomial Logit Models](https://mlsanity.com/paper/2301.12254/) (2023)
- [Stochastic Matching Bandits with Rare Optimization Updates](https://mlsanity.com/paper/2509.04194/) (2025)
- [Oracle-Efficient Combinatorial Semi-Bandits](https://mlsanity.com/paper/2510.21431/) (2025)

## Abstract (arXiv)

We consider the dynamic assortment optimization problem under the multinomial logit model (MNL) with unknown utility parameters. The main question investigated in this paper is model mis-specification under the varepsilon-contamination model, which is a fundamental model in robust statistics and machine learning. In particular, throughout a selling horizon of length T, we assume that customers make purchases according to a well specified underlying multinomial logit choice model in a (1-varepsilon)-fraction of the time periods, and make arbitrary purchasing decisions instead in the remaining varepsilon-fraction of the time periods. In this model, we develop a new robust online assortment optimization policy via an active elimination strategy. We establish both upper and lower bounds on the regret, and show that our policy is optimal up to logarithmic factor in T when the assortment capacity is constant. %% capacity of assortments has a constant upper limit. We further develop a fully adaptive policy that does not require any prior knowledge of the contamination parameter varepsilon. In the case of the existence a sub-optimality gap between optimal and sub-optimal products, we also established gap-dependent logarithmic regret upper bounds and lower bounds in both the known-varepsilon and unknown-varepsilon cases. Our simulation study shows that our policy outperforms the existing policies based on upper confidence bounds (UCB) and Thompson sampling.