Click-Based MNL: Algorithmic Frameworks for Modeling Click Data in Assortment Optimization

Abstract

We introduce the click-based MNL choice model, a novel framework for capturing customer purchasing decisions in e-commerce settings. We augment the classical Multinomial Logit choice model with the assumption that customers only consider the items they have clicked on before they proceed to compare their random utilities. We propose a simple estimation framework that leverages clickstream data and machine learning classification algorithms. We study the resulting assortment optimization problem, where the objective is to select a subset of products, made available for purchase, to maximize the expected revenue. Our main algorithmic contribution comes in the form of a polynomial-time approximation scheme (PTAS) for this problem, showing that the optimal expected revenue can be efficiently approached within any degree of accuracy. In the course of establishing this result, we develop novel technical ideas, including enumeration schemes and stochastic inequalities, which may be of broader interest. Using data acquired in collaboration with Alibaba, we fit click-based MNL and Mixed MNL models to historical sales and click data in a setting where the online platform must present customized six-product displays to users. We show that our approach significantly outperforms the Mixed MNL models in terms of out-of-sample predictive accuracy, and the computational cost of its estimation process is smaller by an order of magnitude.