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Solution Theory of Hamilton-Jacobi-Bellman Equations in Spectral Barron Spaces (2503.18656v1)
Published 24 Mar 2025 in math.AP
Abstract: We study the solution theory of the whole-space static (elliptic) Hamilton-Jacobi-BeLLMan (HJB) equation in spectral Barron spaces. We prove that under the assumption that the coefficients involved are spectral Barron functions and the discount factor is sufficiently large, there exists a sequence of uniformly bounded spectral Barron functions that converges locally uniformly to the solution. As a consequence, the solution of the HJB equation can be approximated by two-layer neural networks without curse of dimensionality.