A special formulation of the Schrödinger problem consists in minimizing some action on the
Wasserstein space of probability measures on a Riemannian manifold subject to fixed initial
and final data. We extend this action minimization problem by replacing the usual entropy,
underlying the Schrödinger problem, with a general function on the Wasserstein space. The
corresponding minimal cost approaches the squared Wasserstein distance when the
fluctuation parameter ε tends to zero. We show heuristically that the solutions satisfy some …