Dynamic Assortment Selection and Pricing with Learning
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Primary Area: reinforcement learning
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Keywords: assortment selection, pricing, dynamic, learning, optimal, regret, multinomial logit, contextual
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TL;DR: We propose an optimal algorithm for dynamic assortment selection and pricing that learns from user feedback to maximize revenue.
Abstract: We consider a dynamic assortment selection and pricing problem in which a seller has $n$ different items available for sale. In each round, the seller observes $d$-dimensional contextual preference information 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 a 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 $n$-independent revenue regret of order $\widetilde{\mathcal{O}}(d \sqrt{T})$. We also show that this regret rate is optimal, up to logarithmic factors, by obtaining lower bounds for the regret achievable by any algorithm.
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Submission Number: 7896
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