Variational Inference for Stochastic Control of Infinite Dimensional Systems

Abstract: This paper develops a variational inference framework for control of infinite dimensional stochastic systems. We employ a measure theoretic approach which relies on the generalization of Girsanov's theorem, as well as the relation between relative entropy and free energy. The derived control scheme is applicable to a large class of stochastic, infinite dimensional systems, and can be used for trajectory optimization and model predictive control. Our work opens up new research avenues at the intersection of stochastic control, inference and information theory for dynamical systems described by stochastic partial differential equations.