Sequential Assortment Recommendation under the Impatient Mixed Cascade Model

Abstract

In many recommendation systems, consumers make purchase decisions across multiple pages. This study complements existing research by employing an Impatient Mixed Cascade model to describe consumer decisions. Our model delineates the intra-page decisions of a representative consumer through a cascade model, wherein a specific preference list is drawn from an exogenous distribution. The random number of pages viewed by the consumer is contingent upon their level of patience. In light of the computational complexities associated with estimating the preference list distribution in our proposed model, our primary objective is to formulate a robust recommendation strategy without such knowledge, while concurrently achieving a revenue performance comparable to the optimal revenue of a benchmark endowed with complete information. Our contributions encompass: (1) Demonstrating the efficacy of the sequentially revenue-ordered recommendation strategy in unconstrained settings, highlighting the limits of personalization and the diminishing marginal contribution of consumer patience to platform revenue. (2) Proposing exact or approximation algorithms under different types of recommendation constraints. (3) Devising a learning algorithm with sublinear regret when model parameters are unknown. (4) Demonstrating superior prediction performance of the proposed model over other multi-page choice models using real-world datasets, accompanied by numerical analyses quantifying the robust solution's performance. (5) Extending our results to incorporate the more general Attention-Based Satisficing choice model proposed by \cite{gao2023simple} under the multi-page setting.

Keywords: cascade model, sequential recommendation, assortment optimization, approximation