Online Personalized Assortment Optimization with High-Dimensional Customer Contextual Data

Abstract

Problem definition: Consider an online personalized assortment optimization problem in which customers arrive sequentially and make their decisions (e.g., click an ad, purchase a product) following the multinomial logit choice model with unknown parameters. Utilizing a customer’s personal information that is high-dimensional, the firm selects an assortment tailored for each individual customer’s preference. Academic/practical relevance: High dimensionality of a customer’s contextual information is prevalent in real applications, and it creates tremendous computational challenge in online personalized optimization. Methodology: In this paper, an efficient learning algorithm is developed to tackle the computational complexity issue while maintaining satisfactory performance. The algorithm first applies a random projection for dimension reduction and incorporates an online convex optimization procedure for parameter estimation, thus overcoming the issue of linearly increasing computational requirement as data accumulates. Then, it integrates the upper confidence bound method to balance the exploration and revenue exploitation. Results: The theoretical performance of the algorithm in terms of regret is derived under some plausible sparsity assumption on personal information that is observed in real data, and numerical experiments using both synthetic data and a real data set from Yahoo! show that the algorithm performs very well, having scalability and significant advantage in computational time compared with benchmark methods. Managerial implications: Our findings suggest that practitioners should process high-dimensional sparse customer data with an appropriate feature engineering technique, such as random projection (instead of abandoning the sparse portion) to maximize the effectiveness of online optimization algorithms.