Online Assortment and Price Optimization Under Contextual Choice Models
This addresses the challenge of dynamic pricing and assortment selection for e-commerce platforms, offering a novel algorithm with theoretical guarantees, though it is incremental in improving regret bounds for contextual settings.
The paper tackles the problem of online assortment and price optimization under contextual choice models, where a seller learns user preferences to maximize revenue, achieving a revenue regret of order ̃O(d √(KT)/L_0) and providing a lower bound of Ω(d √T/L_0).
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 $Ω(d \sqrt{T}/ L_0)$ for the regret achievable by any algorithm.