Computing Augustin Information via Hybrid Geodesically Convex Optimization
Part Of
IEEE International Symposium on Information Theory - Proceedings
Start Page
2532
End Page
2537
ISBN (of the container)
979-835038284-6
Date Issued
2024-07-07
Author(s)
Abstract
We propose a Riemannian gradient descent with the Poincaré metric to compute the 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 . 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.
Event(s)
2024 IEEE International Symposium on Information Theory (ISIT)
Publisher
IEEE
Type
conference paper