  For stochastic diffusion processes the dominant eigenfunctions of the
corresponding Koopman operator contain important information about the
slow-scale dynamics, that is, about the location and frequency of rare events.
In this article, we reformulate the eigenproblem in terms of $\chi$-functions
in the ISOKANN framework and discuss how optimal control and importance
sampling allows for zero variance sampling of these functions. We provide a new
formulation of the ISOKANN algorithm allowing for a proof of convergence and
incorporate the optimal control result to obtain an adaptive iterative
algorithm alternating between importance sampling and $\chi$-function
approximation. We demonstrate the usage of our proposed method in experiments
increasing the approximation accuracy by several orders of magnitude.
