Abstract
This talk will exploit the equivalence between the Schrödinger Bridge problem and the entropy penalized optimal transport in order to find a different approach to the duality, in the spirit of optimal transport. This approach results in a priori estimates which are consistent in the limit when the regularization parameter goes to zero and also extends to multi-marginal optimal transport.
In particular, this duality approach provide an alternative proof of the convergence of the Sinkhorn algorithm with two marginals and show convergence of the Sinkhorn algorithm in the multi-marginal case.