Modeling Attrition in Recommender Systems with Departing Bandits

Traditionally, when recommender systems are formalized as multi-armed bandits, the policy of the recommender system influences the rewards accrued, but not the length of interaction. However, in real-world systems, dissatisfied users may depart (and never come back). In this work, we propose a novel multi-armed bandit setup that captures such policydependent horizons. Our setup consists of a finite set of user types, and multiple arms with Bernoulli payoffs. Each (user type, arm) tuple corresponds to an (unknown) reward probability. Each user's type is initially unknown and can only be inferred through their response to recommendations. Moreover, if a user is dissatisfied with their recommendation, they might depart the system. We first address the case where all users share the same type, demonstrating that a recent UCBbased algorithm is optimal. We then move forward to the more challenging case, where users are divided among two types. While naive approaches cannot handle this setting, we provide an efficient learning algorithm that achieves Õ( √ T ) regret, where T is the number of users. 1 We denote by [n] the set 1, . . . , n. 2 We formalize the reward as is standard in the online learning literature, from the perspective of the learner. However, defining the reward from the user perspective by, e.g., considering her utility as the number of clicks she gives or the number of articles she reads induces the same model.