In this paper we provide a framework to cope with two problems: (i) the
fragility of reinforcement learning due to modeling uncertainties because of
the mismatch between controlled laboratory/simulation and real-world conditions
and (ii) the prohibitive computational cost of stochastic optimal control. We
approach both problems by using reinforcement learning to solve the stochastic
dynamic programming equation. The resulting reinforcement learning controller
is safe with respect to several types of constraints and it can actively learn
about the modeling uncertainties. Unlike exploration and exploitation, probing
and safety are employed automatically by the controller itself, resulting
real-time learning. A simulation example demonstrates the efficacy of the
proposed approach