Cascade Submodular Maximization: Question Selection and Sequencing in Online Personality Quiz

Abstract

Personality quiz is a powerful tool that enables costumer segmentation by actively asking them questions, and marketers are using it as an effective method of generating leads and increasing e‐commerce sales. We study the problem of how to select and sequence a group of quiz questions so as to optimize the quality of customer segmentation. We assume that the customer will sequentially scan the list of questions. After reading a question, the customer makes two, possibly correlated, random decisions: (i) she first decides whether to answer this question or not, and then (ii) decides whether to continue reading the next question or not. We further assume that the utility of questions that have been answered can be captured by a monotone and submodular function. In general, our problem falls into the category of non‐adaptive active learning‐based customer profiling. Note that under our model, the probability of a question being answered depends on the location of that question, as well as the set of other questions placed ahead of that question, this makes our problem fundamentally different from existing studies on submodular optimization. We develop a series of question selection and sequencing strategies with provable performance bound. Although we focus on the application of quiz design in this study, our results apply to a broad range of applications, including assortment optimization with position bias effect.

Non-monotone Sequential Submodular Maximization

“…These formulations aim to select a subset of items that maximizes a submodular function. However, in many real-world applications, the objective is not only to select items but also to rank them in a specific order (Azar and Gamzu 2011;Tschiatschek, Singla, and Krause 2017;Tang and Yuan 2021b). This motivates the study of sequential submodular maximization (Asadpour et al 2022;Zhang, Tatti, and Gionis 2022), a fundamental problem in submodular optimization.…”

Streaming adaptive submodular maximization

“…These formulations aim to select a subset of items that maximizes a submodular function. However, in many realworld applications, the objective is not only to select items but also to rank them in a specific order (Azar and Gamzu 2011, Tschiatschek et al 2017, Tang and Yuan 2021b.…”