Algorithmic Content Selection and the Impact of User Disengagement

The content selection problem of digital services is often modeled as a decision-process where a service chooses, over multiple rounds, an arm to pull from a set of arms that each return a certain reward. This classical model does not account for the possibility that users disengage when dissatisfied and thus fails to capture an important trade-off between choosing content that promotes future engagement versus immediate reward. In this work, we introduce a model for the content selection problem where dissatisfied users may disengage and where the content that maximizes immediate reward does not necessarily maximize the odds of future user engagement. We show that when the relationship between each arm's expected reward and effect on user satisfaction are linearly related, an optimal content selection policy can be computed efficiently with dynamic programming under natural assumptions about the complexity of the users' engagement patterns. Moreover, we show that in an online learning setting where users with unknown engagement patterns arrive, there is a variant of Hedge that attains a $\tfrac 12$-competitive ratio regret bound. We also use our model to identify key primitives that determine how digital services should weigh engagement against revenue. For example, when it is more difficult for users to rejoin a service they are disengaged from, digital services naturally see a reduced payoff but user engagement may -- counterintuitively -- increase.