Stability of Entropic Optimal Transport and Schrödinger Bridges [article]

Promit Ghosal, Marcel Nutz, Espen Bernton
2022 arXiv   pre-print
We establish the stability of solutions to the entropically regularized optimal transport problem with respect to the marginals and the cost function. The result is based on the geometric notion of cyclical invariance and inspired by the use of c-cyclical monotonicity in classical optimal transport. As a consequence of stability, we obtain the wellposedness of the solution in this geometric sense, even when all transports have infinite cost. More generally, our results apply to a class of
more » ... Schrödinger bridge problems including entropic optimal transport.
arXiv:2106.03670v2 fatcat:evkz2mn4tbgzbbe7xulvrrtjpy