Work

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

Year: 2021

Type: article

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 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.

Source: IEEE Control Systems Letters

DOI: 10.1109/lcsys.2021.3089139

Authors: Maxim Staritsyn, Nikolay Pogodaev, Roman Chertovskih, Fernando Lobo Pereira

Institutions: Universidade do Porto, N.N. Krasovskii Institute of Mathematics and Mechanics of the Ural Branch of the Russian Academy of Sciences, Institute for System Dynamics and Control Theory

Language: English

Topic: Geometric Analysis and Curvature Flows

Subfield: Applied Mathematics

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

Funders: Snap, Russian Science Foundation

Awards: G3088114415, G4987724659, G5822449970