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This paper studies the decision making problem with Funnel Structure. Funnelstructure, a well-known concept in the marketing field, occurs in those systemswhere the decision maker interacts with the environment in a layered mannerreceiving far fewer observations from deep layers than shallow ones. Forexample, in the email marketing campaign application, the layers correspond toOpen, Click and Purchase events. Conversions from Click to Purchase happen veryinfrequently because a purchase cannot be made unless the link in an email isclicked on.  We formulate this challenging decision making problem as a contextual banditwith funnel structure and develop a multi-task learning algorithm thatmitigates the lack of sufficient observations from deeper layers. We analyzeboth the prediction error and the regret of our algorithms. We verify ourtheory on prediction errors through a simple simulation. Experiments on both asimulated environment and an environment based on real-world data from a majoremail marketing company show that our algorithms offer significant improvementover previous methods.

Decision Making Problems with Funnel Structure: A Multi-Task Learning Approach with Application to Email Marketing Campaigns