Separable approximations of optimal value functions and their representation by neural networks
File(s)
Published version
Author(s)
Sperl, Mario
Saluzzi, Luca
Kalise, Dante
Gruene, Lars
Type
Journal Article
Abstract
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.
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.
Date Issued
2026-06-01
Date Acceptance
2025-11-28
Citation
SIAM Journal of Control and Optimization, 2026, 64 (3), pp.1099-1126
ISSN
0363-0129
Publisher
Society for Industrial and Applied Mathematics
Start Page
1099
End Page
1126
Journal / Book Title
SIAM Journal of Control and Optimization
Volume
64
Issue
3
Copyright Statement
Copyright © 2026 Society for Industrial and Applied Mathematics.
License URL
Identifier
10.1137/25M173346X
Subjects
separable approximations
decaying sensitivity
neural networks
optimal control MSC codes. 49L20
68T07
93C41
Publication Status
Published
Date Publish Online
2026-05-07