HR-Bandit: Human-AI Collaborated Linear Recourse Bandit

Human doctors frequently recommend actionable recourses that allow patients to modify their conditions to access more effective treatments. Inspired by such healthcare scenarios, we propose the Recourse Linear UCB ($\textsf{RLinUCB}$) algorithm, which optimizes both action selection and feature modifications by balancing exploration and exploitation. We further extend this to the Human-AI Linear Recourse Bandit ($\textsf{HR-Bandit}$), which integrates human expertise to enhance performance. $\textsf{HR-Bandit}$ offers three key guarantees: (i) a warm-start guarantee for improved initial performance, (ii) a human-effort guarantee to minimize required human interactions, and (iii) a robustness guarantee that ensures sublinear regret even when human decisions are suboptimal. Empirical results, including a healthcare case study, validate its superior performance against existing benchmarks.