Speaker
Description
In this talk, we discuss how separable structures provide an effective approach to approximating high-dimensional optimal value functions. The key structural property that enables such approximations is a decaying sensitivity between subsystems, meaning that the influence of one state variable on another diminishes with their graph-based spatial distance. This property makes it possible to construct separable approximations of the optimal value function as a sum of localized contributions. We further demonstrate that these separable approximations admit efficient neural network representations, where the number of parameters grows only polynomially with the state space dimension. These results highlight how structural properties of the problem can be leveraged to obtain scalable neural network representations, thereby mitigating the curse of dimensionality in optimal control.