arXiv:2606. 08113v1 Announce Type: new Abstract: A small Wasserstein distance does not certify that a transformation is admissible.
arXiv:2412. 20556v2 Announce Type: replace-cross Abstract: We study distributionally robust optimization (DRO) for robust inference when the worst-case distribution is continuous, leading to significant computational challenges due to the infinite-dimensional nature of the optimization problem.
arXiv:2604. 04342v2 Announce Type: replace Abstract: Many data-driven decision problems are formulated using a nominal distribution estimated from historical data, while performance is ultimately determined by a deployment distribution that may be shifted, context-dependent, partially observed, or stress-induced.
arXiv:2605. 09916v2 Announce Type: replace-cross Abstract: We introduce the observable Wasserstein distance, a framework for deriving lower bounds on the Wasserstein distance between probability measures on Polish metric spaces, designed to bypass the computational intractability of exact optimal transport in large-scale, non-Euclidean datasets.
arXiv:2606. 04695v1 Announce Type: new Abstract: High-dimensional optimal transport is seldom available in closed form.
The paper introduces the Wasserstein entropic value-at-risk, a coherent risk measure that replaces the relative-entropy ball of the traditional entropic value-at-risk with an optimal-transport ball. This new measure captures reachable catastrophes that the original entropic measure ignores, and its variational dual mirrors the entropic formula with a transport price replacing inverse temperature. By driving the transport radius with belief entropy, the authors derive a closed‑form robust dynamic‑programming operator whose cautiousness decreases as belief sharpens, providing a certified safety sandwich and a sharp safety switch.
arXiv:2606. 19117v1 Announce Type: cross Abstract: Offline policy learning has received growing attention in causal inference.
arXiv:2410. 01244v2 Announce Type: replace-cross Abstract: We introduce a novel Wasserstein-1 ($W_1$) path-space divergence for stochastic and deterministic dynamics and establish a Wasserstein Uncertainty Propagation (WUP) theorem that bounds the $W_1$ distance between terminal distributions by the proposed divergence, equivalently characterized by a weighted $L^2$ discrepancy between the underlying drifts and the $W_1$ distance between their initial measures.
arXiv:2605. 26078v3 Announce Type: replace Abstract: Wasserstein policy gradient (WPG) is a policy optimization method for reinforcement learning (RL) that exploits the optimal-transport geometry of action distributions.
arXiv:2610.07162v1 Announce Type: new Abstract: Deep hedging learns trading policies from historical or simulated market trajectories, yet under nonstationarity these training paths may not represent...
The paper introduces a geometric framework for reinforcement learning that treats policies as mappings into the Wasserstein space of action probabilities. It establishes a Riemannian structure induced by stationary distributions, defines the tangent space of policies, and characterizes geodesics while addressing measurability concerns. The authors formulate a general RL optimization problem, construct a gradient flow via Otto's calculus, compute the gradient and Hessian of the energy, and demonstrate the approach with numerical examples for low‑dimensional problems and neural‑network‑parameterized policies for high‑dimensional settings.
arXiv:2610. 20743v1 Announce Type: new Abstract: Many modern learning problems require comparing probability distributions whose individual observations are themselves probability measures, naturally giving rise to meta-measures in $\mathcal{P}(\mathcal{P}(\Omega))$.
arXiv:2606. 27767v1 Announce Type: new Abstract: Optimizing functionals over the space of probability measures is now ubiquitous in machine learning.