Scalable Methods for Computing Entropic Gromov-Wasserstein Optimal Transport

This work provides a deep exploration of alternative approaches to solve the continuous Gromov-Wasserstein optimal transport problem based on the use of the entropic regularized reformulation. While previous research has demonstrated the efficacy of adding an entropic regularization term in accelerating convergence in discrete scenarios, its application in the continuous domain is relatively unexplored. A key advantage of incorporating this regularization term lies in its ability to enable sampling of transported vectors from a distribution, rather than relying on approximating the transport map function through neural networks. The neural approach has been previously investigated but introduces challenges due to the complexity of the problem, resulting in unstable network behavior and requiring intricate tuning. In my work two already known methods from regular optimal transport named Energy-guided Entropic Neural Optimal Transport (EgENOT) and Light Schrödinger bridge, are studied and adapted to the Gromov-Wasserstein setup in order to be tested on several experimental setups to determine their performance and/or limitations.