14 citations · 33 across the 24 of their papers we have counts for
32 papers
KL Convergence Guarantees for Score diffusion models under minimal data assumptions
Giovanni Conforti, Alain Durmus, Marta Gentiloni Silveri
Diffusion models are a new class of generative models that revolve around the estimation of the score function associated with a stochastic differential equation. Subsequent to its…
Non-asymptotic convergence bounds for Sinkhorn iterates and their gradients: a coupling approach
Giacomo Greco, Maxence Noble, Giovanni Conforti +1
Computational optimal transport (OT) has recently emerged as a powerful framework with applications in various fields. In this paper we focus on a relaxation of the original OT pro…
Quantitative contraction rates for Sinkhorn's algorithm: beyond bounded costs and compact marginals
Giovanni Conforti, Alain Durmus, Giacomo Greco
We show non-asymptotic exponential convergence of Sinkhorn iterates to the Schrödinger potentials, solutions of the quadratic Entropic Optimal Transport problem on .…
Hamilton--Jacobi equations for controlled gradient flows: cylindrical test functions
Giovanni Conforti, Richard C. Kraaij, Daniela Tonon
This work is the second part of a program initiated in arXiv:2111.13258 aiming at the development of an intrinsic geometric well-posedness theory for Hamilton-Jacobi equations rela…
Mean Field Optimization Problem Regularized by Fisher Information
Julien Claisse, Giovanni Conforti, Zhenjie Ren +1
Recently there is a rising interest in the research of mean field optimization, in particular because of its role in analyzing the training of neural networks. In this paper by add…
Weak semiconvexity estimates for Schrödinger potentials and logarithmic Sobolev inequality for Schrödinger bridges
Giovanni Conforti
We investigate the quadratic Schrödinger bridge problem, a.k.a. Entropic Optimal Transport problem, and obtain weak semiconvexity and semiconcavity bounds on Schrödinger potentials…
Gradient estimates for the Schrödinger potentials: convergence to the Brenier map and quantitative stability
Alberto Chiarini, Giovanni Conforti, Giacomo Greco +1
We show convergence of the gradients of the Schrödinger potentials to the Brenier map in the small-time limit under general assumptions on the marginals, which allow for unbounded…
Hamilton--Jacobi equations for controlled gradient flows: the comparison principle
Giovanni Conforti, Richard Kraaij, Daniela Tonon
Motivated by recent developments in the fields of large deviations for interacting particle system and mean field control, we establish a comparison principle for the Hamilton--Jac…
Entropic turnpike estimates for the kinetic Schrödinger problem
Alberto Chiarini, Giovanni Conforti, Giacomo Greco +1
We investigate the kinetic Schrödinger problem, obtained considering Langevin dynamics instead of Brownian motion in Schrödinger's thought experiment. Under a quasilinearity assump…
Time reversal of Markov processes with jumps under a finite entropy condition
Giovanni Conforti, Christian Léonard
Motivated by entropic optimal transport, time reversal of Markov jump processes in is investigated. Relying on an abstract integration by parts formula for the carré…
Time reversal of diffusion processes under a finite entropy condition
Patrick Cattiaux, Giovanni Conforti, Ivan Gentil +1
Motivated by entropic optimal transport, time reversal of diffusion processes is revisited. An integration by parts formula is derived for the carré du champ of a Markov process in…
A non-linear monotonicity principle and applications to Schrödinger type problems
Julio Backhoff-Veraguas, Mathias Beiglböck, Giovanni Conforti
A basic idea in optimal transport is that optimizers can be characterized through a geometric property of their support sets called cyclical monotonicity. In recent years, similar…
On the variational interpretation of local logarithmic Sobolev inequalities
Gauthier Clerc, Giovanni Conforti, Ivan Gentil
The celebrated Otto calculus has established itself as a powerful tool for proving quantitative energy dissipation estimates and provides with an elegant geometric interpretation o…
Long-time behaviour of entropic interpolations
Gauthier Clerc, Giovanni Conforti, Ivan Gentil
In this article we investigate entropic interpolations. These measure valued curves describe the optimal solutions of the Schr{ö}dinger problem [Sch31], which is the problem of fin…
A probabilistic approach to convex -entropy decay for Markov chains
Giovanni Conforti
We study the exponential dissipation of entropic functionals for continuous time Markov chains and the associated convex Sobolev inequalities, including MLSI and Beckner inequaliti…
Game on Random Environment, Mean-field Langevin System and Neural Networks
Giovanni Conforti, Anna Kazeykina, Zhenjie Ren
In this paper we study a type of games regularized by the relative entropy, where the players' strategies are coupled through a random environment variable. Besides the existence a…
A formula for the time derivative of the entropic cost and applications
Giovanni Conforti, Luca Tamanini
In the recent years the Schrödinger problem has gained a lot of attention because of the connection, in the small-noise regime, with the Monge-Kantorovich optimal transport problem…
The mean field Schrödinger problem: ergodic behavior, entropy estimates and functional inequalities
Julio Backhoff-Veraguas, Giovani Conforti, Ivan Gentil +1
We study the mean field Schrödinger problem (MFSP), that is the problem of finding the most likely evolution of a cloud of interacting Brownian particles conditionally on the obser…
Multi-marginal Schrodinger bridges
Yongxin Chen, Giovanni Conforti, Tryphon T. Georgiou +1
We consider the problem to identify the most likely flow in phase space, of (inertial) particles under stochastic forcing, that is in agreement with spatial (marginal) distribution…
Around the entropic Talagrand inequality
Giovanni Conforti, Luigia Ripani
In this article we study generalization of the classical Talagrand transport-entropy inequality in which the Wasserstein distance is replaced by the entropic transportation cost. T…
Conditioned point processes with application to Lévy bridges
Giovanni Conforti, Tetiana Kosenkova, Sylvie Roelly
Our first result concerns a characterisation by means of a functional equation of Poisson point processes conditioned by the value of their first moment. It leads to a generalised…
Measure-valued spline curves: an optimal transport viewpoint
Yongxin Chen, Giovanni Conforti, Tryphon T. Georgiou
The aim of this article is to introduce and address the problem to smoothly interpolate (empirical) probability measures. To this end, we lift the concept of a spline curve from th…
Extremal flows on Wasserstein space
Giovanni Conforti, Michele Pavon
We develop an intrinsic geometric approach to calculus of variations on Wasserstein space. We show that the flows associated to the Schroedinger bridge with general prior, to Optim…
Approximating conditional distributions
Alberto Chiarini, Alessandra Cipriani, Giovanni Conforti
In this article, we discuss the basic ideas of a general procedure to adapt the Stein-Chen method to bound the distance between conditional distributions. From an integration-by-pa…