From Few-Shot Optimal Control to Few-Shot Learning

2025/03/17 by Chertovskih, Roman, Pogodaev, Nikolay, Staritsyn, Maxim +1
#FOS: Mathematics #Numerical Analysis (math.NA) #Optimization and Control (math.OC)

paper · doi:10.48550/arxiv.2503.13298

Abstract

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.

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