Systems and Control Perspectives on Hybrid Learning and Neurosymbolic Artificial Intelligence

We consider inference, control and decision making in single-agent or multi-agent dynamical systems, where the dynamical systems are hybrid automata, and the metrics and specifications involve hybrid variables, i.e. both Boolean and numerical variables. We first describe the great variety of applications that lead to such problems including autonomous cars and large scale smart robo-cab systems, sensor networks, to next generation hybrid terrestrial and non-terrestrial networks, smart energy systems, medical diagnosis problems, smart manufacturing systems, scheduling in modern semiconductor manufacturing foundries, network security and trust. The complexity of such autonomous systems necessitates the efficient integration of domain knowledge based methods with data driven methods, i.e. machine learning (ML) and artificial intelligence methods. We identify several key challenges in these problems: achieving high performance with limited data samples, unsupervised and supervised ML with hybrid variables, multi-criteria based AI, risk and performance duality and its relationship to efficient sampling and large deviations theory, novel model predictive problems with hybrid systems and on graphs, efficient integration of domain specific LLMs with Knowledge Graphs (KGs). We demonstrate how trade-off analysis via multi-objective optimization, with hybrid variables, can play an important role in solving such problems. We describe such methods and algorithms as examples of homotopy optimization with hybrid variables. We describe how the resulting algorithms relate closely to Neurosymbolic AI.