| Autor: |
Luu, Hoang Phuc Hau, Yu, Hanlin, Williams, Bernardo, Mikkola, Petrus, Hartmann, Marcelo, Puolamäki, Kai, Klami, Arto |
| Rok vydání: |
2024 |
| Předmět: |
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| Druh dokumentu: |
Working Paper |
| Popis: |
We study a class of optimization problems in the Wasserstein space (the space of probability measures) where the objective function is \emph{nonconvex} along generalized geodesics. When the regularization term is the negative entropy, the optimization problem becomes a sampling problem where it minimizes the Kullback-Leibler divergence between a probability measure (optimization variable) and a target probability measure whose logarithmic probability density is a nonconvex function. We derive multiple convergence insights for a novel {\em 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. |
| Databáze: |
arXiv |
| Externí odkaz: |
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