This paper presents a novel user experience optimization concept and method, named User Experience Sensor, applied within the Hybrid Intelligence System (HINT). The HINT system, defined as a combination of an extensive AI system and the possibility of attaching a human expert, is designed to be used by relational agents, which may have a physical form, such as a robot, a kiosk, be embodied in an avatar, or may also exist as only software. The proposed method focuses on automatic process evaluation as a common sensor for optimization of the user experience for every process stage and the indicator for human-expert automatic session activation. This functionality is realized by the User Experience Sensor, which constitutes one of main elements of the self-optimizing interaction system. The authors present the optimization mechanism of the HINT system as an analogy to the process of building a Tower of Hanoi. The proposed sensor evaluates the user experience and measures the user/employee efficiency at every stage of a given process, offering the user to choose other forms of information, interaction, or expert support. The designed HINT system is able to learn and self-optimize, making the entire process more intuitive and easy for each and every user individually. The HINT system with the proposed sensor, implemented in a window assembly facility, successfully reduced assembly time, increased employees' satisfaction, and assembly quality. The proposed approach can be implemented in numerous man-machine interaction applications.