Strategic Linear Contextual Bandits

TL;DR

This paper introduces a new mechanism for linear contextual bandits that incentivizes truthful reporting from strategic agents, balancing regret minimization with truthful behavior in a setting where agents may game the system.

Contribution

The paper proposes the Optimistic Grim Trigger Mechanism (OptGTM), a novel approach combining mechanism design with online learning to handle strategic misreporting in linear bandits.

Findings

OptGTM incentivizes truthful reporting of contexts.

Failing to account for strategic behavior leads to linear regret.

There is an inherent trade-off between mechanism design and regret minimization.

Abstract

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.