PDPO: Parametric Density Path Optimization
Fuente:
arXiv
Salvato in:
| Autori principali: | , , |
|---|---|
| Natura: | Preprint |
| Pubblicazione: |
2025
|
| Soggetti: | |
| Accesso online: | |
| Tags: |
Aggiungi Tag
Nessun Tag, puoi essere il primo ad aggiungerne!!
|
| _version_ | 1866912750492450816 |
|---|---|
| author | Hernandez, Sebastian Gutierrez Chen, Peng Zhou, Haomin |
| author_facet | Hernandez, Sebastian Gutierrez Chen, Peng Zhou, Haomin |
| contents | We introduce Parametric Density Path Optimization (PDPO), a novel method for computing action-minimizing paths between probability densities. The core idea is to represent the target probability path as the pushforward of a reference density through a parametric map, transforming the original infinite-dimensional optimization over densities to a finite-dimensional one over the parameters of the map. We derive a static formulation of the dynamic problem of action minimization and propose cubic spline interpolation of the path in parameter space to solve the static problem. Theoretically, we establish an error bound of the action under proper assumptions on the regularity of the parameter path. Empirically, we find that using 3-5 control points of the spline interpolation suffices to accurately resolve both multimodal and high-dimensional problems. We demonstrate that PDPO can flexibly accommodate a wide range of potential terms, including those modeling obstacles, mean-field interactions, stochastic control, and higher-order dynamics. Our method outperforms existing state-of-the-art approaches in benchmark tasks, demonstrating superior computational efficiency and solution quality. The source code will be publically available after the revision process. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_18473 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | PDPO: Parametric Density Path Optimization Hernandez, Sebastian Gutierrez Chen, Peng Zhou, Haomin Optimization and Control We introduce Parametric Density Path Optimization (PDPO), a novel method for computing action-minimizing paths between probability densities. The core idea is to represent the target probability path as the pushforward of a reference density through a parametric map, transforming the original infinite-dimensional optimization over densities to a finite-dimensional one over the parameters of the map. We derive a static formulation of the dynamic problem of action minimization and propose cubic spline interpolation of the path in parameter space to solve the static problem. Theoretically, we establish an error bound of the action under proper assumptions on the regularity of the parameter path. Empirically, we find that using 3-5 control points of the spline interpolation suffices to accurately resolve both multimodal and high-dimensional problems. We demonstrate that PDPO can flexibly accommodate a wide range of potential terms, including those modeling obstacles, mean-field interactions, stochastic control, and higher-order dynamics. Our method outperforms existing state-of-the-art approaches in benchmark tasks, demonstrating superior computational efficiency and solution quality. The source code will be publically available after the revision process. |
| title | PDPO: Parametric Density Path Optimization |
| topic | Optimization and Control |
| url | https://arxiv.org/abs/2505.18473 |