  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.
