Wasserstein Formulation of Reinforcement Learning. An Optimal Transport Perspective on Policy Optimization

ArXi:2604.14765v1 Announce Type: new We present a geometric framework for Reinforcement Learning (RL) that views policies as maps into the Wasserstein space of action probabilities. First, we define a Riemannian structure induced by stationary distributions, proving its existence in a general context. We then define the tangent space of policies and characterize the geodesics, specifically addressing the measurability of vector fields mapped from the state space to the tangent space of probability measures over the action space.