OmniMechanism Design for Human-AI Collaboration with Impressionable Minds

As AI systems are increasingly deployed in high-stakes domains such as healthcare, effectively integrating human expertise with AI outputs is critical for reliable decision-making. A substantial body of theoretical work studies optimal mechanisms for human-AI collaboration (HAC), focusing on when to involve humans and how to combine their expertise with AI predictions. However, these approaches largely overlook a key factor highlighted by empirical evidence: human judgments are impressionable and can vary depending on how AI outputs are presented. For example, when AI systems defer decisions to humans, revealing or withholding the AI prediction can significantly influence human judgments. Moreover, existing work neglects deployment-time variability, where conditions, particularly the cost of eliciting human input, may differ substantially from those observed during training. To address these challenges, we introduce a rigorous and theoretically grounded framework for human-AI collaboration, termed \emph{collaborative omnimechanism design}, based on a novel and computationally efficient contextual bandit variant of boosting for outcome indistinguishability. In particular, we reduce a calibration-type outcome indistinguishability condition to projected smooth calibration, providing novel time-efficiency result, bypassing the high-dimension curse induced by complicated collaboration methods. Our framework provides a principled characterization of human impressionability and introduces a unified optimization scheme that enables robust and adaptable decision-making across diverse query costs and evaluation objectives without retraining. We further validate our theoretical results through comprehensive experiments.