Information Geometry of Exponentiated Gradient: Convergence beyond L-Smoothness
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arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2025
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| _version_ | 1866909569334116352 |
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| author | Elshiaty, Yara Vanmaele, Ferdinand Petra, Stefania |
| author_facet | Elshiaty, Yara Vanmaele, Ferdinand Petra, Stefania |
| contents | We study the minimization of smooth, possibly nonconvex functions over the positive orthant, a key setting in Poisson inverse problems, using the exponentiated gradient (EG) method. Interpreting EG as Riemannian gradient descent (RGD) with the $e$-Exp map from information geometry as a retraction, we prove global convergence under weak assumptions -- without the need for $L$-smoothness -- and finite termination of Riemannian Armijo line search. Numerical experiments, including an accelerated variant, highlight EG's practical advantages, such as faster convergence compared to RGD based on interior-point geometry. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_05136 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Information Geometry of Exponentiated Gradient: Convergence beyond L-Smoothness Elshiaty, Yara Vanmaele, Ferdinand Petra, Stefania Optimization and Control We study the minimization of smooth, possibly nonconvex functions over the positive orthant, a key setting in Poisson inverse problems, using the exponentiated gradient (EG) method. Interpreting EG as Riemannian gradient descent (RGD) with the $e$-Exp map from information geometry as a retraction, we prove global convergence under weak assumptions -- without the need for $L$-smoothness -- and finite termination of Riemannian Armijo line search. Numerical experiments, including an accelerated variant, highlight EG's practical advantages, such as faster convergence compared to RGD based on interior-point geometry. |
| title | Information Geometry of Exponentiated Gradient: Convergence beyond L-Smoothness |
| topic | Optimization and Control |
| url | https://arxiv.org/abs/2504.05136 |