Separable approximations of optimal value functions under a decaying sensitivity assumption

TL;DR

This paper introduces a method to efficiently approximate optimal value functions in interconnected control systems by leveraging decaying sensitivities, allowing for scalable neural network-based solutions without the curse of dimensionality.

Contribution

It presents a novel approach that exploits decaying sensitivities to construct separable approximations, reducing complexity in interconnected optimal control problems.

Findings

Enables curse-of-dimensionality free approximation

Uses neural networks for scalable solutions

Demonstrates effectiveness under decaying sensitivity assumptions

Abstract

An efficient approach for the construction of separable approximations of optimal value functions from interconnected optimal control problems is presented. The approach is based on assuming decaying sensitivities between subsystems, enabling a curse-of-dimensionality free approximation, for instance by deep neural networks.