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Online Assortment and Price Optimization Under Contextual Choice Models

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  • Yigit Efe Erginbas
  • Thomas A. Courtade
  • Kannan Ramchandran

Abstract

We consider an assortment selection and pricing problem in which a seller has $N$ different items available for sale. In each round, the seller observes a $d$-dimensional contextual preference information vector for the user, and offers to the user an assortment of $K$ items at prices chosen by the seller. The user selects at most one of the products from the offered assortment according to a multinomial logit choice model whose parameters are unknown. The seller observes which, if any, item is chosen at the end of each round, with the goal of maximizing cumulative revenue over a selling horizon of length $T$. For this problem, we propose an algorithm that learns from user feedback and achieves a revenue regret of order $\widetilde{O}(d \sqrt{K T} / L_0 )$ where $L_0$ is the minimum price sensitivity parameter. We also obtain a lower bound of order $\Omega(d \sqrt{T}/ L_0)$ for the regret achievable by any algorithm.

Suggested Citation

  • Yigit Efe Erginbas & Thomas A. Courtade & Kannan Ramchandran, 2025. "Online Assortment and Price Optimization Under Contextual Choice Models," Papers 2503.11819, arXiv.org.
    • Handle: RePEc:arx:papers:2503.11819
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    References listed on IDEAS

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    3. Omar Besbes & Assaf Zeevi, 2009. "Dynamic Pricing Without Knowing the Demand Function: Risk Bounds and Near-Optimal Algorithms," Operations Research, INFORMS, vol. 57(6), pages 1407-1420, December.
    4. Shipra Agrawal & Vashist Avadhanula & Vineet Goyal & Assaf Zeevi, 2019. "MNL-Bandit: A Dynamic Learning Approach to Assortment Selection," Operations Research, INFORMS, vol. 67(5), pages 1453-1485, September.
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