Modeling Attrition in Recommender Systems with Departing Bandits

TL;DR

This paper introduces a new bandit model for recommender systems that accounts for user departure due to dissatisfaction, providing algorithms with optimal or near-optimal regret bounds for different user type scenarios.

Contribution

It proposes a novel bandit framework incorporating user departure, and develops efficient algorithms with provable regret bounds for single and multiple user types.

Findings

Optimal UCB-based algorithm for single user type.

Efficient learning algorithm for two user types with $ ilde{O}( oot{2}T)$ regret.

Addresses policy-dependent horizons in recommender systems.

Abstract

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 policy-dependent 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 UCB-based 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 $\tilde{O}(\sqrt{T})$ regret, where $T$ is the number of users.