From Few-Shot Optimal Control to Few-Shot Learning

We present an approach to solving unconstrained nonlinear optimal control problems for a broad class of dynamical systems. This approach involves lifting the nonlinear problem to a linear ``super-problem'' on a dual Banach space, followed by a non-standard ``exact'' variational analysis, -- culminating in a descent method that achieves rapid convergence with minimal iterations. We investigate the applicability of this framework to mean-field control and discuss its perspectives for the analysis of information propagation in self-interacting neural networks.