5 papers
A PDE approach to Benamou--Brenier formula for the Schrödinger problem
Mattia Garatti, Luca Nenna, Simona Rota Nodari +1
We studied the Benamou--Brenier formulation of the Schrödinger problem, focusing on a gap between theoretical results and applications, that often involve measures with unbounded…
Hessian stability and convergence rates for entropic and Sinkhorn potentials via semiconcavity
Giacomo Greco, Luca Tamanini
In this paper we determine quantitative stability bounds for the Hessian of entropic potentials, \ie, the dual solution to the entropic optimal transport problem. To the authors' k…
A semiconcavity approach to stability of entropic plans and exponential convergence of Sinkhorn's algorithm
Alberto Chiarini, Giovanni Conforti, Giacomo Greco +1
We study stability of optimizers and convergence of Sinkhorn's algorithm for the entropic optimal transport problem. In the special case of the quadratic cost, our stability bounds…
The Riemannian geometry of Sinkhorn divergences
Hugo Lavenant, Jonas Luckhardt, Gilles Mordant +2
We propose a new metric between probability measures on a compact metric space that mirrors the Riemannian manifold-like structure of quadratic optimal transport but includes entro…
The infimal convolution structure of the Hellinger-Kantorovich distance
Nicolò De Ponti, Giacomo Enrico Sodini, Luca Tamanini
We show that the Hellinger-Kantorovich distance can be expressed as the metric infimal convolution of the Hellinger and the Wasserstein distances, as conjectured by Liero, Mielke,…