Feedback Maximum Principle for Ensemble Control of Local Continuity Equations: An Application to Supervised Machine Learning

• Type: Article in International Scientific Journal
• Date: 2022

Authors

Staritsyn, M (Author) FEUP; Nikolay Pogodaev (Author) Other; Roman Chertovskih (Author) FEUP; Fernando Lobo Pereira (Author) FEUP

Journal

Title: IEEE Control Systems Letters

Vol. 6

Pages: 1046-1051

Publisher: IEEE

Indexing

ISI Web of Knowledge - 5 Citations

Scopus - 7 Citations

Other information

Authenticus ID: P-00V-28R

DOI: 10.1109/lcsys.2021.3089139

Abstract (EN): 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 conditions of optimality which involve feedback controls inherent to the extremal structure designed via the standard Pontryagin's Maximum Principle. These optimality conditions admit 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.

Language: English

Type (Professor's evaluation): Scientific

No. of pages: 6