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Separable approximations of optimal value functions and their representation by neural networks

Title data

Sperl, Mario ; Saluzzi, Luca ; Kalise, Dante ; Grüne, Lars:
Separable approximations of optimal value functions and their representation by neural networks.
Bayreuth , 2025 . - 20 p.
DOI: https://doi.org/10.48550/arXiv.2502.08559

Official URL: Volltext

Project information

Project title:
Project's official title
Project's id
Curse-of-dimensionality-free nonlinear optimal feedback control with deep neural networks. A compositionality-based approach via Hamilton-Jacobi-Bellman PDEs
463912816

Project financing: Deutsche Forschungsgemeinschaft

Abstract in another language

The use of separable approximations is proposed to mitigate the curse of dimensionality related to the approximation of high-dimensional value functions in optimal control. The separable approximation exploits intrinsic decaying sensitivity properties of the system, where the influence of a state variable on another diminishes as their spatial, temporal, or graph-based distance grows. This property allows the efficient representation of global functions as a sum of localized contributions. A theoretical framework for constructing separable approximations in the context of optimal control is proposed by leveraging decaying sensitivity in both discrete and continuous time. Results extend prior work on decay properties of solutions to Lyapunov and Riccati equations, offering new insights into polynomial and exponential decay regimes. Connections to neural networks are explored, demonstrating how separable structures enable scalable representations of high-dimensional value functions while preserving computational efficiency.

Further data

Item Type: Preprint, postprint
Keywords: Separable approximations; Decaying sensitivity; Neural Networks; Optimal control
Subject classification: MSC codes: 49L20, 68T07, 93C41
Institutions of the University: Faculties
Faculties > Faculty of Mathematics, Physics und Computer Science
Faculties > Faculty of Mathematics, Physics und Computer Science > Department of Mathematics
Faculties > Faculty of Mathematics, Physics und Computer Science > Department of Mathematics > Chair Mathematics V (Applied Mathematics)
Faculties > Faculty of Mathematics, Physics und Computer Science > Department of Mathematics > Chair Mathematics V (Applied Mathematics) > Chair Mathematics V (Applied Mathematics) - Univ.-Prof. Dr. Lars Grüne
Faculties > Faculty of Mathematics, Physics und Computer Science > Department of Mathematics > Chair Applied Mathematics
Profile Fields
Profile Fields > Advanced Fields
Profile Fields > Advanced Fields > Nonlinear Dynamics
Result of work at the UBT: Yes
DDC Subjects: 500 Science > 510 Mathematics
Date Deposited: 14 Feb 2025 10:13
Last Modified: 14 Feb 2025 10:13
URI: https://eref.uni-bayreuth.de/id/eprint/92358