The Entropic regularization of the classical quadratic optimal transport control problem (aka Schr¨odinger problem) can be
extended first to solve numerically drift controlled diffusion processes Benamou et al. (2018).
Then in a second part he showed how time discretisation of the relative entropy can be used
to characterize the (linear) time scaling under which the relative entropy between diffusion
processes becomes a divergence between the diffusion coefficients of its arguments instead of
blowing up when they are singular. This object is also known as “Specific Relative Entropy”.
Then classical Entropic optimal numerical methods, like Sinkhorn, are generalised to diffusion
controlled diffusion processes.