Strategic Linear Contextual Bandits
This work addresses the challenge of strategic manipulation in online learning systems, which is crucial for applications like recommender systems, though it appears to be an incremental contribution at the intersection of mechanism design and bandit algorithms.
The paper tackles the problem of strategic agents misreporting contexts in linear contextual bandits, such as in recommender systems, and proposes the Optimistic Grim Trigger Mechanism (OptGTM) to incentivize truthful reporting while minimizing regret, showing that ignoring strategic behavior leads to linear regret.
Motivated by the phenomenon of strategic agents gaming a recommender system to maximize the number of times they are recommended to users, we study a strategic variant of the linear contextual bandit problem, where the arms can strategically misreport privately observed contexts to the learner. We treat the algorithm design problem as one of mechanism design under uncertainty and propose the Optimistic Grim Trigger Mechanism (OptGTM) that incentivizes the agents (i.e., arms) to report their contexts truthfully while simultaneously minimizing regret. We also show that failing to account for the strategic nature of the agents results in linear regret. However, a trade-off between mechanism design and regret minimization appears to be unavoidable. More broadly, this work aims to provide insight into the intersection of online learning and mechanism design.