Non-geodesically-convex optimization in the Wasserstein space
Fuente:
arXiv
Gespeichert in:
| Hauptverfasser: | , , , , , , |
|---|---|
| Format: | Preprint |
| Veröffentlicht: |
2024
|
| Schlagworte: | |
| Online-Zugang: | |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| _version_ | 1866909450197008384 |
|---|---|
| author | Luu, Hoang Phuc Hau Yu, Hanlin Williams, Bernardo Mikkola, Petrus Hartmann, Marcelo Puolamäki, Kai Klami, Arto |
| author_facet | Luu, Hoang Phuc Hau Yu, Hanlin Williams, Bernardo Mikkola, Petrus Hartmann, Marcelo Puolamäki, Kai Klami, Arto |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2406_00502 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Non-geodesically-convex optimization in the Wasserstein space Luu, Hoang Phuc Hau Yu, Hanlin Williams, Bernardo Mikkola, Petrus Hartmann, Marcelo Puolamäki, Kai Klami, Arto Optimization and Control Machine Learning 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. |
| title | Non-geodesically-convex optimization in the Wasserstein space |
| topic | Optimization and Control Machine Learning |
| url | https://arxiv.org/abs/2406.00502 |