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Langevin diffusion processes and their discretizations are often used for sampling from a target density. The most convenient framework for assessing the quality of such a sampling scheme corresponds to smooth and strongly log-concave…

Probability · Mathematics 2018-12-27 Arnak S. Dalalyan , Lionel Riou-Durand

Flow Matching has become a cornerstone of modern generative models like Stable Diffusion 3, largely due to the efficiency of its Rectified Flow (RF) variant. The success of RF hinges on iteratively learning straight trajectories, pushing…

Machine Learning · Computer Science 2026-05-19 Vansh Bansal , Saptarshi Roy , Purnamrita Sarkar , Alessandro Rinaldo

We study the rate of convergence w.r.t.~a Wasserstein type distance for random walk approximations of mean field BSDEs. Our method does not use the particle method but instead a freezing technique. We extend results by Briand, Ch. Geiss, S.…

Probability · Mathematics 2025-05-21 Boualem Djehiche , Hannah Geiss , Stefan Geiss , Céline Labart , Jani Nykänen

This paper presents an algorithm tailored for the efficient recovery of sparse probability measures incorporating $\ell_0$-sparse regularization within the probability simplex constraint. Employing the Bregman proximal gradient method, our…

Optimization and Control · Mathematics 2024-11-26 Jianting Pan , Ming Yan

In this work, we examine sampling problems with non-smooth potentials. We propose a novel Markov chain Monte Carlo algorithm for sampling from non-smooth potentials. We provide a non-asymptotical analysis of our algorithm and establish a…

Machine Learning · Computer Science 2022-02-11 Jiaming Liang , Yongxin Chen

This paper discusses the efficiency of Hybrid Primal-Dual (HPD) type algorithms to approximate solve discrete Optimal Transport (OT) and Wasserstein Barycenter (WB) problems, with and without entropic regularization. Our first contribution…

Optimization and Control · Mathematics 2022-09-01 Antonin Chambolle , Juan Pablo Contreras

We study the multivariate deconvolution problem of recovering the distribution of a signal from independent and identically distributed observations additively contaminated with random errors (noise) from a known distribution. For errors…

Statistics Theory · Mathematics 2023-09-28 Judith Rousseau , Catia Scricciolo

The Wasserstein barycenter problem seeks a probability measure that minimizes the weighted average of the Wasserstein distances to a given collection of probability measures. We study the discrete setting, where each measure has finite…

Optimization and Control · Mathematics 2025-11-07 Jiaqi Wang , Weijun Xie

Non-convex sampling is a key challenge in machine learning, central to non-convex optimization in deep learning as well as to approximate probabilistic inference. Despite its significance, theoretically there remain many important…

Machine Learning · Computer Science 2024-09-18 Mohammad Reza Karimi , Ya-Ping Hsieh , Andreas Krause

Distributionally-robust optimization is often studied for a fixed set of distributions rather than time-varying distributions that can drift significantly over time (which is, for instance, the case in finance and sociology due to…

Optimization and Control · Mathematics 2020-10-01 Iman Shames , Farhad Farokhi

We study the Riemannian Langevin Algorithm for the problem of sampling from a distribution with density $\nu$ with respect to the natural measure on a manifold with metric $g$. We assume that the target density satisfies a log-Sobolev…

Machine Learning · Computer Science 2022-04-25 Khashayar Gatmiry , Santosh S. Vempala

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…

Machine Learning · Computer Science 2026-01-28 Dai Hai Nguyen , Duc Dung Nguyen , Atsuyoshi Nakamura , Hiroshi Mamitsuka

In this paper, we study the problem of sampling from a distribution under the constraint of differential privacy (DP). Prior works measure the utility of DP sampling with density ratio-based measures such as KL divergence. However, such…

Machine Learning · Statistics 2026-05-12 Shokichi Takakura , Seng Pei Liew , Satoshi Hasegawa

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…

Machine Learning · Computer Science 2026-05-27 Zhaoyu Zhu , Rui Gao , Shuang Li

We study the reknown deconvolution problem of recovering a distribution function from independent replicates (signal) additively contaminated with random errors (noise), whose distribution is known. We investigate whether a Bayesian…

Statistics Theory · Mathematics 2021-11-15 Judith Rousseau , Catia Scricciolo

When minimizing a multiobjective optimization problem (MOP) using multiobjective gradient descent methods, the imbalances among objective functions often decelerate the convergence. In response to this challenge, we propose two types of the…

Optimization and Control · Mathematics 2023-08-10 Jian Chen , Liping Tang , Xinmin Yang

We study the problem of minimizing a relatively-smooth convex function using stochastic Bregman gradient methods. We first prove the convergence of Bregman Stochastic Gradient Descent (BSGD) to a region that depends on the noise (magnitude…

Optimization and Control · Mathematics 2021-04-21 Radu-Alexandru Dragomir , Mathieu Even , Hadrien Hendrikx

In this paper, we study a method to sample from a target distribution $\pi$ over $\mathbb{R}^d$ having a positive density with respect to the Lebesgue measure, known up to a normalisation factor. This method is based on the Euler…

Statistics Theory · Mathematics 2016-12-20 Alain Durmus , Eric Moulines

Optimization over the space of probability measures endowed with the Wasserstein-2 geometry is central to modern machine learning and mean-field modeling. However, traditional methods relying on full Wasserstein gradients often suffer from…

Machine Learning · Statistics 2026-04-03 Yewei Xu , Qin Li

Sampling from various kinds of distributions is an issue of paramount importance in statistics since it is often the key ingredient for constructing estimators, test procedures or confidence intervals. In many situations, the exact sampling…

Computation · Statistics 2016-12-06 Arnak S. Dalalyan