# Sharp Inequalities for f-divergences

arXiv: https://arxiv.org/abs/1302.0336 · HTML: https://mlsanity.com/paper/1302.0336/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 2 Feb 2013.

## Built on by (most cited first, 3 of 3)

- [Information-Theoretic Bounds on the Moments of the Generalization Error of Learning Algorithms](https://mlsanity.com/paper/2102.02016/) (2021)
- [Chained Generalisation Bounds](https://mlsanity.com/paper/2203.00977/) (2022)
- [The Fourier Discrepancy Function](https://mlsanity.com/paper/2102.02979/) (2021)

## Abstract (arXiv)

f-divergences are a general class of divergences between probability measures which include as special cases many commonly used divergences in probability, mathematical statistics and information theory such as Kullback-Leibler divergence, chi-squared divergence, squared Hellinger distance, total variation distance etc. In this paper, we study the problem of maximizing or minimizing an f-divergence between two probability measures subject to a finite number of constraints on other f-divergences. We show that these infinite-dimensional optimization problems can all be reduced to optimization problems over small finite dimensional spaces which are tractable. Our results lead to a comprehensive and unified treatment of the problem of obtaining sharp inequalities between f-divergences. We demonstrate that many of the existing results on inequalities between f-divergences can be obtained as special cases of our results and we also improve on some existing non-sharp inequalities.