arXiv:2610. 12740v1 Announce Type: cross Abstract: We study the two-sample estimation of the powered Sliced Wasserstein functional under projected $r$-th moment assumptions.
arXiv:2610.35490v1 Announce Type: cross Abstract: We study minimax rates for conditional generative learning under integrated Wasserstein loss, with H\"older continuous conditional laws and an unrest...
The paper investigates quantile distributional policy evaluation by approximating the return distribution under a policy with a quantile Bellman fixed point. It constructs an estimator from an empirical Markov decision process and derives non‑asymptotic error bounds in Wasserstein distances, achieving root‑n rates that are independent of the quantile resolution for a wide range of Wasserstein orders. The authors also characterize the exact local asymptotic minimax risk and show that their estimator attains this optimal rate, while examining how the risk depends on resolution in simple state‑space examples.
arXiv:2606. 06384v2 Announce Type: replace-cross Abstract: The sub-Gaussian parameter (also called the variance proxy) of a mean-zero random variable $X$ is defined as $\xi^2_\star = \sup_{\lambda \in \mathbb{R}} L(\lambda)$ where $L(\lambda) = \frac{2}{\lambda^2} \log \mathbb{E} e^{\lambda X}$ is a weighted cumulant generating function.
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.
arXiv:2610. 08883v1 Announce Type: cross Abstract: Finding low-energy configurations of interacting particles and approximating probability distributions lead to the minimization of potential-interaction energies in Wasserstein space.
arXiv:2609.27546v1 Announce Type: cross Abstract: Score-based diffusion models are increasingly considered in settings where the underlying data distribution may differ from the training distribution...
arXiv:2502. 17602v2 Announce Type: replace-cross Abstract: We study a class of stochastic nonsmooth optimization problems in which an outer variable minimizes the expectation of a pointwise maximum.
arXiv:2606. 27767v1 Announce Type: new Abstract: Optimizing functionals over the space of probability measures is now ubiquitous in machine learning.
arXiv:2511.07414v2 Announce Type: replace-cross Abstract: The quantity of interest in the classical Cram\'er-Rao theory of unbiased estimation (e.g., the Cram\'er-Rao lower bound, its exact attainmen...
arXiv:2610. 19773v1 Announce Type: new Abstract: Score-based generative models driven by $\alpha$-stable L{\'e}vy processes have been proposed as an alternative to Brownian diffusion models, with empirical evidence suggesting improved sampling and better modeling of heavy-tailed data.
arXiv:2608. 06283v1 Announce Type: new Abstract: We study the problem of sampling from target distributions whose potentials are simultaneously non-smooth, subject to superlinear gradient growth, and non-convex.
The paper introduces a distributionally robust method for learning hyperparameters of first‑order convex optimization algorithms. By minimizing a Wasserstein‑robust performance estimation problem over a dataset of problem instances, the approach interpolates between classical learning‑to‑optimize (L2O) and worst‑case PEP design. The authors solve the resulting problem with stochastic gradient descent, provide high‑probability risk bounds, and demonstrate that the learned algorithms outperform both worst‑case optimal and vanilla L2O baselines on logistic regression, LASSO, and linear programming tasks.