  Consider a platform that wants to learn a personalized policy for each user,
but the platform faces the risk of a user abandoning the platform if she is
dissatisfied with the actions of the platform. For example, a platform is
interested in personalizing the number of newsletters it sends, but faces the
risk that the user unsubscribes forever. We propose a general thresholded
learning model for scenarios like this, and discuss the structure of optimal
policies. We describe salient features of optimal personalization algorithms
and how feedback the platform receives impacts the results. Furthermore, we
investigate how the platform can efficiently learn the heterogeneity across
users by interacting with a population and provide performance guarantees.
