Freezing the Geometry, Adapting the Dynamics: Minimum Action Distance in Non-Stationary Environments

We present a decomposition of the distance between two states that transfers across changes in environment dynamics. We use the Minimum Action Distance (MAD) as an invariant layer that counts the fewest decision steps between two states and depends only on the support of the transition kernel. We learn the MAD encoder once, then fit an action model $f_\psi(z, a)$ on its latent states z, which carries the transition probabilities and adapts online. On a two-path corridor where the chance of an action succeeding differs between two symmetric routes we show that a latent model-predictive planner with horizon 6 on a 22-step route chooses the correct shortest route after each of 21 switches in transition probabilities.