Wasserstein
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Related Articles from SNS
Well-Posed KL-Regularized Control via Wasserstein and Kalman-Wasserstein KL Divergences
arXiv:2602.02250v2 Announce Type: replace-cross Abstract: Kullback-Leibler (KL) divergence regularization is widely used in reinforcement learning, but it becomes infinite under support mismatch and can degenerate in low-noise regimes. Using a unified information-geometric framework, we introduce KL analogs by replacing the Fisher-Rao geometry in the dynamical formulation of the KL with transport-based geometries, and derive closed-form expressions for common distribution families. Between...
Accelerated Multiple Wasserstein Gradient Flows for Multi-objective Distributional Optimization
arXiv:2601.19220v2 Announce Type: replace Abstract: We study multi-objective optimization over probability distributions in Wasserstein space. Recently, Nguyen et al. (2025) introduced Multiple Wasserstein Gradient Descent (MWGraD) algorithm, which exploits the geometric structure of Wasserstein space to jointly optimize multiple objectives. Building on this approach, we propose an accelerated variant, A-MWGraD, inspired by Nesterov's acceleration.
Wasserstein normalized autoencoder for anomaly detection
Announce Type: replace-cross Abstract: A novel anomaly detection algorithm is presented. The Wasserstein normalized autoencoder (WNAE) is a normalized probabilistic model that minimizes the Wasserstein distance between the learned probability distribution--a Boltzmann distribution where the energy is the reconstruction error of the autoencoder--and the distribution of the training data. This algorithm has been developed and applied to the identification of semivisible jets--conical sprays of...
A Unifying View of Variational Generative Wasserstein Flows
arXiv:2605.31369v1 Announce Type: new Abstract: Many modern generative models can be viewed as minimizing divergences between probability distributions, yet they rely on different algorithmic and geometric principles. Wasserstein gradient flows provide a continuous-time formulation for optimizing over distributions, and can be approximated through their implicit discretization via the Jordan-Kinderlehrer-Otto (JKO) scheme. In this work, we present a unified theoretical framework for...
On the Wasserstein Geodesic Principal Component Analysis of probability measures
arXiv:2506.04480v2 Announce Type: replace-cross Abstract: This paper focuses on Geodesic Principal Component Analysis (GPCA) on a collection of probability distributions using the Otto-Wasserstein geometry. The goal is to identify geodesic curves in the space of probability measures that best capture the modes of variation of the underlying dataset. We first address the case of a collection of Gaussian distributions, and show how to lift the computations in the space of invertible linear maps.
Global Convergence of Wasserstein Policy Gradient for Entropy-Regularized Reinforcement Learning
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. For the entropy-regularized RL objective, WPG evolves each state-conditional policy by transporting it along the action gradient of the soft Q-function together with a Langevin-type diffusion. Despite its appeal for continuous-control problems, its global convergence properties remain poorly...
Wasserstein Contraction of Coordinate Ascent Variational Inference
arXiv:2605.30253v2 Announce Type: replace-cross Abstract: We study the contraction in Wasserstein distance of the coordinate ascent variational inference algorithm. This is shown to hold under a transport-information inequality at the fixed points and a functional smoothness condition. The results are general and sharp, allow for local convergence guarantees, hold for general smooth manifolds, and also in some non-smooth spaces.
A Temporal Spatial Minimax Rate for Smoothly-Varying Distributions in Wasserstein Space
arXiv:2606.07325v1 Announce Type: cross Abstract: We study the minimax rate of estimating a future value $\mu_{t_n+h}$ of a curve $t\mapsto\mu_t$ in the $2$-Wasserstein space $\mathcal{P}_2(\mathbb{R}^d)$ from finitely many noisy snapshots of its past, under an adiabatic bound $\|\nabla_t^k v\|\le\varepsilon$ on the $k$-th covariant derivative of the velocity field. Our central result is a unified temporal-spatial minimax lower bound: over regular, locally transport-rich subclasses, every...
Variable-preconditioned transformed primal-dual method for generalized Wasserstein Gradient Flows
arXiv:2509.15385v3 Announce Type: replace Abstract: We propose a Variable-Preconditioned Transformed Primal-Dual (VPTPD) method for solving generalized Wasserstein gradient flows based on the structure-preserving JKO scheme. This is a nontrivial extension of the TPD method [Chen et al. incorporating proximal splitting techniques to address the challenges arising from the nonsmoothness of the objective function.
On the regularization of Wasserstein GANs
Announce Type: replace-cross Abstract: Since their invention, generative adversarial networks (GANs) have become a popular approach for learning to model a distribution of real (unlabeled) data. Convergence problems during training are overcome by Wasserstein GANs which minimize the distance between the model and the empirical distribution in terms of a different metric, but thereby introduce a Lipschitz constraint into the optimization problem. A simple way to enforce the Lipschitz...