Many cyber-physical-human systems (CPHS) involve a human decision-maker who may receive recommendations from an artificial intelligence (AI) platform while holding the ultimate responsibility of making decisions. In such CPHS applications, the human decision-maker may depart from an optimal recommended decision and instead implement a different one for various reasons. In this letter, we develop a rigorous framework to overcome this challenge. In our framework, we consider that humans may deviate from AI recommendations as they perceive and interpret the system's state in a different way than the AI platform. We establish the structural properties of optimal recommendation strategies and develop an approximate human model (AHM) used by the AI. We provide theoretical bounds on the optimality gap that arises from an AHM and illustrate the efficacy of our results in a numerical example.

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