Donato Vásquez

Universidad de Chile

Machine Learning has achieved remarkable success in numerically solving complex problems. This progress has attracted considerable interest within the mathematical community, particularly in the application of machine learning techniques to compute optimal feedback laws. This task is known to suffer from the “curse of dimensionality”, namely, the exponential growth of the computational complexity with the dimensionality of the underlying dynamical system. This phenomenon is particularly important for the numerical resolution of control problems involving partial differential equations, as precise approximations require solving large finite-dimensional control problems.

In these lectures, we will focus on applications of machine learning techniques to the synthesis of optimal feedback laws and study how they can mitigate the curse of dimensionality.  Both supervised and unsupervised techniques will be considered, and their theoretical and practical aspects will be compared. Furthermore, we will provide conditions which ensure the synthesis of approximate optimal feedback laws by these methods, supported by illustrative numerical experiments. This will allow participants to determine the potential and limitations of machine learning in the context of optimal control.