Multi-page Menu Recommendation in Cascade Model with Externalities

Abstract

In this paper, we consider a variant of the cascade model of customer behavior, where the customer browses through a multi-page menu, scanning each page from top to the bottom predominantly. Each page is assigned items belonging to a specific class out of a set of such classes. He/she adopts the first most attractive content, which generates some revenue. We aim at maximizing the total revenue by finding an optimal index-based policy for ranking the content when the customer preferences and patience levels are known. When we have no prior information about the customer, we design the Online Greedy Algorithm (OGA) which we prove to be asymptotically converging to the optimal solution with probability one. We also provide high probability finite-time convergence bounds for the same.