Related papers: Generalized differentiation in Wasserstein space a…
In this article, we derive first-order necessary optimality conditions for a constrained optimal control problem formulated in the Wasserstein space of probability measures. To this end, we introduce a new notion of localised metric…
We investigate a dynamic inverse problem using a regularization which implements the so-called Wasserstein-$1$ distance. It naturally extends well-known static problems such as lasso or total variation regularized problems to a (temporally)…
We study distributionally robust optimization (DRO) problems with uncertainty sets consisting of high-dimensional random vectors that are close in the multivariate Wasserstein distance to a reference random vector. We give conditions when…
In this article, we provide sufficient conditions under which the controlled vector fields solution of optimal control problems formulated on continuity equations are Lipschitz regular in space. Our approach involves a novel combination of…
We obtain the comparison principle for discontinuous viscosity sub- and supersolutions of nonlocal Hamilton-Jacobi equations, with superlinear and coercive gradient terms. The nonlocal terms are integro-differential operators in L\'evy…
In this paper we introduce a Wasserstein-type distance on the set of Gaussian mixture models. This distance is defined by restricting the set of possible coupling measures in the optimal transport problem to Gaussian mixture models. We…
We introduce a distributionally robust maximum likelihood estimation model with a Wasserstein ambiguity set to infer the inverse covariance matrix of a $p$-dimensional Gaussian random vector from $n$ independent samples. The proposed model…
Generalized Wasserstein distances allow to quantitatively compare two continuous or atomic mass distributions with equal or different total mass. In this paper, we propose four numerical methods for the approximation of three different…
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…
Given multiple source domains, domain generalization aims at learning a universal model that performs well on any unseen but related target domain. In this work, we focus on the domain generalization scenario where domain shifts occur among…
We propose of an improved version of the ubiquitous symmetrization inequality making use of the Wasserstein distance between a measure and its reflection in order to quantify the symmetry of the given measure. An empirical bound on this…
We present a novel multiscale framework for analyzing sequences of probability measures in Wasserstein spaces over Euclidean domains. Exploiting the intrinsic geometry of optimal transport, we construct a multiscale transform applicable to…
This paper presents a novel Wasserstein distributionally robust control and state estimation algorithm for partially observable linear stochastic systems, where the probability distributions of disturbances and measurement noises are…
An initial-and boundary-value problem for the Kelvin-Voigt system, modeling a mixture of n incompressible and viscoelastic fluids, with non-constant density, is investigated in this work. The existence of global-in-time weak solutions is…
Wasserstein distributionally robust optimization (DRO) has gained prominence in operations research and machine learning as a powerful method for achieving solutions with favorable out-of-sample performance. Two compelling explanations for…
In this paper we establish an attainability result for the minimum time function of a control problem in the space of probability measures endowed with Wasserstein distance. The dynamics is provided by a suitable controlled continuity…
We study a stochastic control problem on a bounded domain, which arises from a continuous-time optimal management model. Via the corresponding Hamilton-Jacobi-Bellman equation the value function is shown to be jointly continuous and to…
In this paper, we consider the convergence rate with respect to Wasserstein distance in the invariance principle for deterministic nonuniformly hyperbolic systems, where both discrete time systems and flows are included. Our results apply…
Derived from the concentration-compactness principle, the concept of generalized minimizer can be used to define generalized solutions of variational problems which may have components ``infinitely'' distant from each other. In this article…
We develop a general theoretical framework for optimal probability density control on standard measure spaces, aimed at addressing large-scale multi-agent control problems. In particular, we establish a maximum principle (MP) for control…