4 papers
Weak optimal transport with moment constraints: constraint qualification, dual attainment and entropic regularization
Guillaume Carlier, Hugo Malamut, Maxime Sylvestre
We consider weak optimal problems (possibly entropically penalized) incorporating both soft and hard (including the case of the martingale condition) moment constraints. Even in th…
A synthetic approach to comparison principles for variational problems, with applications to optimal transport
Flavien Léger, Maxime Sylvestre
We develop a synthetic, variational framework for deriving comparison principles in infinite-dimensional Banach spaces. Unlike traditional approaches that rely on the regularity of…
On a class of adversarial classification problems which admit a continuous solution
Guillaume Carlier, Maxime Sylvestre
We consider a class of adversarial classification problems in the form of zero-sum games between a classifier and an adversary. The latter is able to corrupt data, at the expense o…
Global Regularity Estimates for Optimal Transport via Entropic Regularisation
Nathael Gozlan, Maxime Sylvestre
We develop a general approach to prove global regularity estimates for quadratic optimal transport using the entropic regularisation of the problem and the Prekopa-Leindler inequal…