Computing Augustin Information via Hybrid Geodesically Convex Optimization
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arXiv
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| Autori principali: | , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866917662017191936 |
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| author | Wang, Guan-Ren Tsai, Chung-En Cheng, Hao-Chung Li, Yen-Huan |
| author_facet | Wang, Guan-Ren Tsai, Chung-En Cheng, Hao-Chung Li, Yen-Huan |
| contents | We propose a Riemannian gradient descent with the Poincaré metric to compute the order-$α$ Augustin information, a widely used quantity for characterizing exponential error behaviors in information theory. We prove that the algorithm converges to the optimum at a rate of $\mathcal{O}(1 / T)$. As far as we know, this is the first algorithm with a non-asymptotic optimization error guarantee for all positive orders. Numerical experimental results demonstrate the empirical efficiency of the algorithm. Our result is based on a novel hybrid analysis of Riemannian gradient descent for functions that are geodesically convex in a Riemannian metric and geodesically smooth in another. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2402_02731 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Computing Augustin Information via Hybrid Geodesically Convex Optimization Wang, Guan-Ren Tsai, Chung-En Cheng, Hao-Chung Li, Yen-Huan Information Theory Optimization and Control We propose a Riemannian gradient descent with the Poincaré metric to compute the order-$α$ Augustin information, a widely used quantity for characterizing exponential error behaviors in information theory. We prove that the algorithm converges to the optimum at a rate of $\mathcal{O}(1 / T)$. As far as we know, this is the first algorithm with a non-asymptotic optimization error guarantee for all positive orders. Numerical experimental results demonstrate the empirical efficiency of the algorithm. Our result is based on a novel hybrid analysis of Riemannian gradient descent for functions that are geodesically convex in a Riemannian metric and geodesically smooth in another. |
| title | Computing Augustin Information via Hybrid Geodesically Convex Optimization |
| topic | Information Theory Optimization and Control |
| url | https://arxiv.org/abs/2402.02731 |