@inproceedings{
luu2024nongeodesicallyconvex,
title={Non-geodesically-convex optimization in the Wasserstein space},
author={Hoang Phuc Hau Luu and Hanlin Yu and Bernardo Williams and Petrus Mikkola and Marcelo Hartmann and Kai Puolam{\"a}ki and Arto Klami},
booktitle={The Thirty-eighth Annual Conference on Neural Information Processing Systems},
year={2024},
url={https://openreview.net/forum?id=LGG1IQhbOr}
}
We study a class of optimization problems in the Wasserstein space (the space of probability measures) where the objective function is nonconvex along generalized geodesics. Specifically, the objective exhibits some difference-of-convex structure along these geodesics. The setting also encompasses sampling problems where the logarithm of the target distribution is difference-of-convex. We derive multiple convergence insights for a novel semi Forward-Backward Euler scheme under several nonconvex (and possibly nonsmooth) regimes. Notably, the semi Forward-Backward Euler is just a slight modification of the Forward-Backward Euler whose convergence is---to our knowledge---still unknown in our very general non-geodesically-convex setting.
Non-geodesically-convex optimization in the Wasserstein space
Hoang Phuc Hau Luu Hanlin Yu Bernardo Williams Petrus Mikkola Marcelo Hartmann Kai Puolamäki Arto Klami