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This paper develops a variational inference framework for control of infinitedimensional stochastic systems. We employ a measure theoretic approach whichrelies on the generalization of Girsanov's theorem, as well as the relationbetween relative entropy and free energy. The derived control scheme isapplicable to a large class of stochastic, infinite dimensional systems, andcan be used for trajectory optimization and model predictive control. Our workopens up new research avenues at the intersection of stochastic control,inference and information theory for dynamical systems described by stochasticpartial differential equations.

Variational Inference for Stochastic Control of Infinite Dimensional Systems