B1789
Title: Doubly high-dimensional contextual bandits: An interpretable model for joint assortment-pricing
Authors: Junhui Jeffrey Cai - University of Notre Dame (United States) [presenting]
Ran Chen - Massachusetts Institute of Technology (United States)
Martin Wainwright - Massachusetts Institute of Technology (United States)
Linda Zhao - University of Pennsylvania (United States)
Abstract: Key challenges in running a retail business include how to select products to present to consumers (the assortment problem), and how to price products (the pricing problem) to maximize revenue or profit. Instead of considering these problems in isolation, a joint approach is proposed to assortment pricing based on contextual bandits. The model is doubly high-dimensional, in that both context vectors and actions are allowed to take values in high-dimensional spaces. In order to circumvent the curse of dimensionality, a simple, flexible model is proposed that captures the interactions between covariates and actions via a (near) low-rank representation matrix. The resulting class of models is reasonably expressive while interpretable through latent factors, and includes various structured linear bandit and pricing models as particular cases. A computationally tractable procedure is proposed, combining an exploration/exploitation protocol with an efficient low-rank matrix estimator, and proven bounds on its regret. Simulation results show that this method has lower regret than state-of-the-art methods applied to various standard bandit and pricing models. Real-world case studies on the assortment-pricing problem, from an industry-leading instant noodles company to an emerging beauty start-up, underscore the gains achievable using the method. At least three-fold gains are shown in revenue or profit, as well as the interpretability of the latent factor models that are learned.
