Robust Dynamic Assortment Optimization in the Presence of Outlier Customers
Xi Chen, Akshay Krishnamurthy, Yining Wang
Operations Research · 2024 · Volume 72 · Issue 3
Abstract
We consider the dynamic assortment optimization problem under the multinomial logit model with unknown utility parameters. The main question investigated in this paper is model mis-specification under the ε -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 − 𝜀 ) ( 1 − ε ) -fraction of the time periods and make arbitrary purchasing decisions instead in the remaining ε -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 we show that our policy is optimal up to a logarithmic factor in T when the assortment capacity is constant. We further develop a fully adaptive policy that does not require any prior knowledge of the contamination parameter ε . In the case of the existence of a suboptimality gap between optimal and suboptimal products, we also established gap-dependent logarithmic regret upper bounds and lower bounds in both the known- ε and unknown- ε cases. Our simulation study shows that our policy outperforms the existing policies based on upper confidence bounds and Thompson sampling. Funding: X. Chen acknowledges support from the National Science Foundation [Grant IIS-1845444]. Supplemental Material: The supplementary material is available at https://doi.org/10.1287/opre.2020.0281 .
Keywords
Machine Learning and Data Science, dynamic assortment optimization, gap-dependent analysis, regret analysis, robustness, active elimination
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