Fast Algorithms for Online Personalized Assortment Optimization in a Big Data Regime

Abstract

We consider an online personalized assortment optimization problem where customers arrive sequentially and make their choices (e.g., click an ad, purchase a product) following the multinomial logit (MNL) model with unknown parameters. Utilizing customer's personal information, the firm makes an assortment decision tailored for the individual customer's preference. We develop two algorithms which make assortment recommendations to maximize expected total revenue while concurrently learning the demand. The first algorithm constructs upper-confidence bounds (UCB) of product utilities using estimated demand parameters and personalized data to balance exploration and exploitation. The second algorithm incorporates a fast online convex optimization procedure in the first algorithm, which significantly reduces the computational effort; thus it is particularly useful when solving online personalized assortment optimization problem in a big data regime. We show that the algorithms can be modified to solve high dimensional problem (i.e., when the dimension of customer's personal information data is high) through a dimension reduction method known as random projection. The theoretical performance for our algorithms in terms of regret are derived, and numerical experiments using synthetic and real data demonstrate that they perform very well in both low and high dimensional settings compared with several benchmarks.