A Sinkhorn-type Algorithm for Constrained Optimal Transport

arXiv:2403.05054v1 Announce Type: cross
Abstract: Entropic optimal transport (OT) and the Sinkhorn algorithm have made it practical for machine learning practitioners to perform the fundamental task of calculating transport distance between statistical distributions. In this work, we focus on a general class of OT problems under a combination of equality and inequality constraints. We derive the corresponding entropy regularization formulation and introduce a Sinkhorn-type algorithm for such constrained OT problems supported by theoretical guarantees. We first bound the approximation error …

abstract algorithm arxiv class combination constraints cs.lg equality focus general inequality machine machine learning math.oc practical statistical transport type work