# Computing Augustin Information via Hybrid Geodesically Convex Optimization

arXiv: https://arxiv.org/abs/2402.02731 · HTML: https://mlsanity.com/paper/2402.02731/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 5 Feb 2024.

## Built on by (most cited first, 1 of 1)

- [Retraction-Based Gradient Projection Algorithms on Manifolds](https://mlsanity.com/paper/2609.30885/) (2026)

## Abstract (arXiv)

We propose a Riemannian gradient descent with the Poincar'e 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 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.