Inference for Adapted Wasserstein Profiles under Policy Reoptimization

We study the smallest time-respecting change of a process law needed to move an optimized multistage value by a prescribed amount. This inverse adapted-Wasserstein profile is an operational robustness margin. Policy reoptimization makes its local geometry asymmetric: improvement is governed by the largest active adapted-score norm, while deterioration is governed by the minimum-norm point in the active-score hull. For finitely many active policies, both coefficients reduce to a Gram matrix and a simplex program. We give a cross-fitted orthogonal Gram estimator with root-$n$ Gaussian behavior and derive the generally non-Gaussian directional limits of the profile coefficients. A controlled tied-policy study validates the geometry and regular inference; a fixed-policy building study illustrates the resulting non-anticipative perturbations.