Neural optimal controller for stochastic systems via pathwise HJB operator

arXiv:2402.15592v1 Announce Type: cross
Abstract: The aim of this work is to develop deep learning-based algorithms for high-dimensional stochastic control problems based on physics-informed learning and dynamic programming. Unlike classical deep learning-based methods relying on a probabilistic representation of the solution to the Hamilton--Jacobi--Bellman (HJB) equation, we introduce a pathwise operator associated with the HJB equation so that we can define a problem of physics-informed learning. According to whether the optimal control has an explicit representation, two numerical methods are …

abstract aim algorithms arxiv control cs.lg deep learning dynamic equation hamilton math.oc physics physics-informed programming representation solution stochastic systems type via work