Feedback maximum principle for ensemble control of local continuity equations. An application to supervised machine learning
Abstract
We consider an optimal control problem for a system of local continuity equations on a space of probability measures. Such systems can be viewed as macroscopic models of ensembles of non-interacting particles or homotypic individuals, representing several different ``populations''. For the stated problem, we propose a necessary optimality condition, which involves feedback controls inherent to the extremal structure, designed via the standard Pontryagin's Maximum Principle conditions. This optimality condition admits a realization as an iterative algorithm for optimal control. As a motivating case, we discuss an application of the derived optimality condition and the consequent numeric method to a problem of supervised machine learning via dynamic systems.
Cite
@article{arxiv.2105.04248,
title = {Feedback maximum principle for ensemble control of local continuity equations. An application to supervised machine learning},
author = {Maxim Staritsyn and Nikolay Pogodaev and Roman Chertovskih and Fernando Lobo Pereira},
journal= {arXiv preprint arXiv:2105.04248},
year = {2021}
}