Feedback maximum principle for ensemble control of local continuity equations. An application to supervised machine learning

• Main Authors: Staritsyn, Maxim, Pogodaev, Nikolay, Chertovskih, Roman, Pereira, Fernando Lobo
• Format: Journal Article
• Language: English
• Published: 10-05-2021
• Subjects: Mathematics - Mathematical Physics; Mathematics - Optimization and Control; Physics - Mathematical Physics
• DOI: 10.48550/arxiv.2105.04248

IEEE Control Systems Letters, vol. 6, pp. 1046-1051, 2022 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.