  Imitation learning methods have demonstrated considerable success in teaching
autonomous systems complex tasks through expert demonstrations. However, a
limitation of these methods is their lack of interpretability, particularly in
understanding the specific task the learning agent aims to accomplish. In this
paper, we propose a novel imitation learning method that combines Signal
Temporal Logic (STL) inference and control synthesis, enabling the explicit
representation of the task as an STL formula. This approach not only provides a
clear understanding of the task but also allows for the incorporation of human
knowledge and adaptation to new scenarios through manual adjustments of the STL
formulae. Additionally, we employ a Generative Adversarial Network
(GAN)-inspired training approach for both the inference and the control policy,
effectively narrowing the gap between the expert and learned policies. The
effectiveness of our algorithm is demonstrated through two case studies,
showcasing its practical applicability and adaptability.
