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math.OC2022★ 2 cited
Displacement smoothness of entropic optimal transport
Guillaume Carlier, Lénaïc Chizat, Maxime Laborde
The function that maps a family of probability measures to the solution of the dual entropic optimal transport problem is known as the Schrödinger map. We prove that when the cost…
math.OC2022★ 1 cited
Mean-Field Langevin Dynamics: Exponential Convergence and Annealing
Lénaïc Chizat
Noisy particle gradient descent (NPGD) is an algorithm to minimize convex functions over the space of measures that include an entropy term. In the many-particle limit, this algori…
math.OC2021★ 3 cited
Convergence Rates of Gradient Methods for Convex Optimization in the Space of Measures
Lénaïc Chizat
We study the convergence rate of Bregman gradient methods for convex optimization in the space of measures on a -dimensional manifold. Under basic regularity assumptions, we sho…