Robust Dynamic Assortment Optimization in the Presence of Outlier Customers

Xi Chen (), Akshay Krishnamurthy () and Yining Wang ()
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Xi Chen: Stern School of Business, New York University, New York, New York 10012
Akshay Krishnamurthy: Machine Learning Group, Microsoft Research New York City, New York, New York 10011
Yining Wang: Naveen Jindal School of Management, University of Texas at Dallas, Richardson, Texas 75080

Operations Research, 2024, vol. 72, issue 3, 999-1015

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 ) -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.

Keywords: Machine Learning and Data Science; dynamic assortment optimization; gap-dependent analysis; regret analysis; robustness; active elimination (search for similar items in EconPapers)
Date: 2024
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