  Systems involving Partial Differential Equations (PDEs) have recently become
more popular among the machine learning community. However prior methods
usually treat infinite dimensional problems in finite dimensions with Reduced
Order Models. This leads to committing to specific approximation schemes and
subsequent derivation of control laws. Additionally, prior work does not
consider spatio-temporal descriptions of noise that realistically represent the
stochastic nature of physical systems. In this paper we suggest a new
reinforcement learning framework that is mostly model-free for Stochastic PDEs
with additive spacetime noise, based on variational optimization in infinite
dimensions. In addition, our algorithm incorporates sparse representations that
allow for efficient learning of feedback policies in high dimensions. We
demonstrate the efficacy of the proposed approach with several simulated
experiments on a variety of SPDEs.
