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

Titelangaben

Sperl, Mario ; Saluzzi, Luca ; Kalise, Dante ; Grüne, Lars:
Separable approximations of optimal value functions and their representation by neural networks.
In: SIAM Journal on Control and Optimization. Bd. 64 (2026) . - S. 1099-1126.
ISSN 1095-7138
DOI: https://doi.org/10.1137/25M173346X

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Abstract

The use of separable approximations is proposed to mitigate the curse of dimen-sionality related to the approximation of high-dimensional value functions in optimal control. Theseparable approximation exploits intrinsic decaying sensitivity properties of the system, where the in-fluence of a state variable on another diminishes as their spatial, temporal, or graph-based distancegrows. This property allows the efficient representation of global functions as a sum of localizedcontributions. A theoretical framework for constructing separable approximations in the contextof optimal control is proposed by leveraging decaying sensitivity in both discrete and continuoustime. Results extend prior work on decay properties of solutions to Lyapunov and Riccati equa-tions, offering new insights into polynomial and exponential decay regimes. Connections to neuralnetworks are explored, demonstrating how separable structures enable scalable representations ofhigh-dimensional value functions while preserving computational efficiency.