Computing Augustin Information via Hybrid Geodesically Convex Optimization
<|reference_start|>Computing Augustin Information via Hybrid Geodesically Convex Optimization: We propose a Riemannian gradient descent with the Poincar\'e metric to compute the order-$\alpha$ 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.<|reference_end|>
@article{wang2024computing,
    title={Computing Augustin Information via Hybrid Geodesically Convex
  Optimization},
    author={Guan-Ren Wang and Chung-En Tsai and Hao-Chung Cheng and Yen-Huan Li},
    journal={arXiv preprint arXiv:2402.02731},
    year={2024},
    archivePrefix={arXiv},
    eprint={2402.02731},
    primaryClass={cs.IT math.IT math.OC}
}