Theoretical Foundations of Homotopy Optimization for Hybrid Learning

This tutorial explores the fundamentals of hybrid learning, highlighting recent advancements in homotopy optimization methods as a foundation for real-time data-driven inference and control. It introduces the Online Deterministic Annealing (ODA) method, a homotopy optimization technique that can be used to estimate the modes of a hybrid model through a sequence of bifurcation phenomena. This enables real-time training of hybrid learning models using adaptive two-timescale stochastic approximation algorithms. The tutorial underscores the significance of hybrid learning as a structural framework for analyzing robustness, explainability, and resource efficiency in data-driven inference and control. Practical applications in hybrid system identification, memory-efficient reinforcement learning, and learning-based control are also discussed.