A Lagrangian description of particles can be represented by the evolution of the probability density, i.e., the Liouville PDE. In the sense of optimal transport on the Wasserstein spaces constrained by finite dimensional dynamical systems, stochastic optimal control will be reformulated to the Liouville PDE and the Bellman equation for reinforcement learning. The well-posedness of control regularization is proved in the sense of minimum attention with open questions for closed-loop stability. Some case studies of application are introduced, 1) synchronization of neuronal excitability, 2) diagnosis of cancer metastasis with clinical CT/MRI, 3) appreciation of diversity in African ancestry and reduction of bias in statistical learning of health disparity