Deep generalized schrödinger bridge
Abstract Mean-Field Game (MFG) serves as a crucial mathematical framework in modeling
the collective behavior of individual agents interacting stochastically with a large population …
the collective behavior of individual agents interacting stochastically with a large population …
Turnpike in optimal control of PDEs, ResNets, and beyond
B Geshkovski, E Zuazua - Acta Numerica, 2022 - cambridge.org
The turnpike property in contemporary macroeconomics asserts that if an economic planner
seeks to move an economy from one level of capital to another, then the most efficient path …
seeks to move an economy from one level of capital to another, then the most efficient path …
Time reversal of diffusion processes under a finite entropy condition
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 an …
integration by parts formula is derived for the carré du champ of a Markov process in an …
Convergence rate of general entropic optimal transport costs
G Carlier, P Pegon, L Tamanini - Calculus of Variations and Partial …, 2023 - Springer
We investigate the convergence rate of the optimal entropic cost v ε to the optimal transport
cost as the noise parameter ε↓ 0. We show that for a large class of cost functions c on R d× …
cost as the noise parameter ε↓ 0. We show that for a large class of cost functions c on R d× …
A formula for the time derivative of the entropic cost and applications
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 …
connection, in the small-noise regime, with the Monge-Kantorovich optimal transport …
Phase transitions, logarithmic Sobolev inequalities, and uniform-in-time propagation of chaos for weakly interacting diffusions
In this article, we study the mean field limit of weakly interacting diffusions for confining and
interaction potentials that are not necessarily convex. We explore the relationship between …
interaction potentials that are not necessarily convex. We explore the relationship between …
Quasi-continuity method for mean-field diffusions: large deviations and central limit theorem
LP Chaintron - arxiv preprint arxiv:2410.04935, 2024 - arxiv.org
A pathwise large deviation principle in the Wasserstein topology and a pathwise central limit
theorem are proved for the empirical measure of a mean-field system of interacting …
theorem are proved for the empirical measure of a mean-field system of interacting …
Controlling conservation laws I: Entropy–entropy flux
We study a class of variational problems for regularized conservation laws with Lax's
entropy-entropy flux pairs. We first introduce a modified optimal transport space based on …
entropy-entropy flux pairs. We first introduce a modified optimal transport space based on …
Quantitative contraction rates for Sinkhorn algorithm: beyond bounded costs and compact marginals
We show non-asymptotic exponential convergence of Sinkhorn iterates to the Schr\" odinger
potentials, solutions of the quadratic Entropic Optimal Transport problem on $\mathbb {R}^ d …
potentials, solutions of the quadratic Entropic Optimal Transport problem on $\mathbb {R}^ d …
Coupling by reflection for controlled diffusion processes: Turnpike property and large time behavior of Hamilton–Jacobi–Bellman equations
G Conforti - The Annals of Applied Probability, 2023 - projecteuclid.org
We investigate the long time behavior of weakly dissipative semilinear Hamilton–Jacobi–
Bellman (HJB) equations and the turnpike property for the corresponding stochastic control …
Bellman (HJB) equations and the turnpike property for the corresponding stochastic control …