Related papers: The Wasserstein Proximal Gradient Algorithm
We propose Drifting Field Policy (DFP), a non-ODE one-step generative policy built on the drifting model paradigm. We frame the policy update as a reverse-KL Wasserstein-2 gradient flow toward a soft target policy, so that each DFP update…
This paper focuses on the contextual optimization problem where a decision is subject to some uncertain parameters and covariates that have some predictive power on those parameters are available before the decision is made. More…
We give a comprehensive description of Wasserstein gradient flows of maximum mean discrepancy (MMD) functionals $\mathcal F_\nu := \text{MMD}_K^2(\cdot, \nu)$ towards given target measures $\nu$ on the real line, where we focus on the…
Gradient descent-ascent (GDA) flows play a central role in finding saddle points of bivariate functionals, with applications in optimization, game theory, and robust control. While they are well-understood in Hilbert and Banach spaces via…
We introduce in this paper two time discretization schemes tailored for a range of Wasserstein gradient flows. These schemes are designed to preserve mass, positivity and to be uniquely solvable. In addition, they also ensure energy…
Wasserstein distance (WD) and the associated optimal transport plan have been proven useful in many applications where probability measures are at stake. In this paper, we propose a new proxy of the squared WD, coined min-SWGG, that is…
We present new algorithms to compute the mean of a set of empirical probability measures under the optimal transport metric. This mean, known as the Wasserstein barycenter, is the measure that minimizes the sum of its Wasserstein distances…
This paper introduces Wasserstein variational inference, a new form of approximate Bayesian inference based on optimal transport theory. Wasserstein variational inference uses a new family of divergences that includes both f-divergences and…
We propose a mathematically principled PDE gradient flow framework for distributionally robust optimization (DRO). Exploiting the recent advances in the intersection of Markov Chain Monte Carlo sampling and gradient flow theory, we show…
The paper considers distributed gradient flow (DGF) for multi-agent nonconvex optimization. DGF is a continuous-time approximation of distributed gradient descent that is often easier to study than its discrete-time counterpart. The paper…
We formulate well-posed continuous-time generative flows for learning distributions that are supported on low-dimensional manifolds through Wasserstein proximal regularizations of $f$-divergences. Wasserstein-1 proximal operators regularize…
We study optimization problems whereby the optimization variable is a probability measure. Since the probability space is not a vector space, many classical and powerful methods for optimization (e.g., gradients) are of little help. Thus,…
Semi-discrete optimal transport problems, which evaluate the Wasserstein distance between a discrete and a generic (possibly non-discrete) probability measure, are believed to be computationally hard. Even though such problems are…
We address the challenge of sequential data-driven decision-making under context distributional uncertainty. This problem arises in numerous real-world scenarios where the learner optimizes black-box objective functions in the presence of…
The purpose of this paper is to answer a few open questions in the interface of kernel methods and PDE gradient flows. Motivated by recent advances in machine learning, particularly in generative modeling and sampling, we present a rigorous…
Wasserstein barycenters provide a geometrically meaningful way to aggregate probability distributions, built on the theory of optimal transport. They are difficult to compute in practice, however, leading previous work to restrict their…
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…
Local optimization presents a promising approach to expensive, high-dimensional black-box optimization by sidestepping the need to globally explore the search space. For objective functions whose gradient cannot be evaluated directly,…
Sampling a probability distribution with an unknown normalization constant is a fundamental problem in computational science and engineering. This task may be cast as an optimization problem over all probability measures, and an initial…
Gromov--Wasserstein (GW) distances compare graphs, shapes, and point clouds through internal distances, without requiring a common coordinate system. This invariance is powerful, but discrete GW is a nonconvex quadratic optimal transport…