Related papers: Optimal transportation and stationary measures for…
We develop the optimal transportation approach to modified log-Sobolev inequalities and to isoperimetric inequalities. Various sufficient conditions for such inequalities are given. Some of them are new even in the classical log-Sobolev…
We study the optimal transport between two probability measures on the real line, where the transport plans are laws of one-step martingales. A quasi-sure formulation of the dual problem is introduced and shown to yield a complete duality…
Human mobility, enabled by diverse transportation modes, is fundamental to urban functionality. Studying these movements across scales-from microscopic to macroscopic-yields valuable insights into urban dynamics. Local adaptation and…
We employ techniques from optimal transport in order to prove decay of transfer operators associated to iterated functions systems and expanding maps, giving rise to a new proof without requiring a Doeblin-Fortet (or Lasota-Yorke)…
We prove a new sample complexity result for divergence regularized optimal transport. Our bound holds for probability measures on~$\mathbb{R}^d$ with exponential tail decay and for radial cost functions that satisfy a local Lipschitz…
We present a self-contained analysis of a particular family of metrics over the set of non-negative integers. We show that these metrics, which are defined through a nested sequence of optimal transport problems, provide tight estimates for…
Many causal parameters depend on a moment of the joint distribution of potential outcomes. Such parameters are especially relevant in policy evaluation settings, where noncompliance is common and accommodated through the model of Imbens &…
Trajectory optimization is a fundamental stochastic optimal control problem. This paper deals with a trajectory optimization approach for dynamical systems subject to measurement noise that can be fitted into linear time-varying stochastic…
We derive distributional limits for empirical transport distances between probability measures supported on countable sets. Our approach is based on sensitivity analysis of optimal values of infinite dimensional mathematical programs and a…
Iterative trajectory optimization techniques for non-linear dynamical systems are among the most powerful and sample-efficient methods of model-based reinforcement learning and approximate optimal control. By leveraging time-variant local…
We employ scoring functions, used in statistics for eliciting risk functionals, as cost functions in the Monge-Kantorovich (MK) optimal transport problem. This gives raise to a rich variety of novel asymmetric MK divergences, which subsume…
Modeling and simulating movement of vehicles in established transportation infrastructures, especially in large urban road networks is an important task. It helps with understanding and handling traffic problems, optimizing traffic…
We study the problem of estimating, in the sense of optimal transport metrics, a measure which is assumed supported on a manifold embedded in a Hilbert space. By establishing a precise connection between optimal transport metrics, optimal…
In this paper, we present a novel iterative Monte Carlo method for approximating the stationary probability of a single state of a positive recurrent Markov chain. We utilize the characterization that the stationary probability of a state…
Here we present an ergodic theorem which adapts a Theorem by J. Elton to the classical thermodynamical formalism and to ergodic transport. First, we discuss how Elton's theorem can be used to characterise Gibbs measures for expanding maps.…
We study the stability of entropically regularized optimal transport with respect to the marginals. Lipschitz continuity of the value and H\"older continuity of the optimal coupling in $p$-Wasserstein distance are obtained under general…
We present a systematic study of conditional triangular transport maps in function spaces from the perspective of optimal transportation and with a view towards amortized Bayesian inference. More specifically, we develop a theory of…
A popular view in contemporary Boltzmannian statistical mechanics is to interpret the measures as typicality measures. In measure-theoretic dynamical systems theory measures can similarly be interpreted as typicality measures. However, a…
We show continuity of the martingale optimal transport optimisation problem as a functional of its marginals. This is achieved via an estimate on the projection in the nested/causal Wasserstein distance of an arbitrary coupling on to the…
Given two probability measures on sequential data, we investigate the transport problem with time-inconsistent preferences in a discrete-time setting. Motivating examples are nonlinear objectives, state-dependent costs, and regularized…