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In this study, we develop a stochastic optimal control approach withreinforcement learning structure to learn the unknown parameters appeared inthe drift and diffusion terms of the stochastic differential equation. Bychoosing an appropriate cost functional, based on a classical optimal feedbackcontrol, we translate the original optimal control problem to a new controlproblem which takes place the unknown parameter as control, and the relatedoptimal control can be used to estimate the unknown parameter. We establish themathematical framework of the dynamic equation for the exploratory state, whichis consistent with the existing results. Furthermore, we consider the linearstochastic differential equation case where the drift or diffusion term withunknown parameter. Then, we investigate the general case where both the driftand diffusion terms contain unknown parameters. For the above cases, we showthat the optimal density function satisfies a Gaussian distribution which canbe used to estimate the unknown parameter. Based on the obtained estimation ofthe parameters, we can do empirical analysis for a given model.

Parameter learning: stochastic optimal control approach with reinforcement learning