# The entropic barrier is n-self-concordant

arXiv: https://arxiv.org/abs/2112.10947 · HTML: https://mlsanity.com/paper/2112.10947/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- Builds on 3 of its 21 references that are in the map.
- First posted on arXiv 21 Dec 2021.

## Builds on (most cited first, 3 of 3)

- [Efficient constrained sampling via the mirror-Langevin algorithm](https://mlsanity.com/paper/2010.16212/) (2020)
- [Exponential ergodicity of mirror-Langevin diffusions](https://mlsanity.com/paper/2005.09669/) (2020)
- [Universal Barrier is n-Self-Concordant](https://mlsanity.com/paper/1809.03011/) (2018)

## Built on by (most cited first, 6 of 6)

- [A Unified Analysis of Nonstochastic Delayed Feedback for Combinatorial Semi-Bandits, Linear Bandits, and MDPs](https://mlsanity.com/paper/2305.08629/) (2023)
- [Algorithmic Aspects of the Log-Laplace Transform and a Non-Euclidean Proximal Sampler](https://mlsanity.com/paper/2302.06085/) (2023)
- [Corruption-Robust Linear Bandits: Minimax Optimality and Gap-Dependent Misspecification](https://mlsanity.com/paper/2410.07533/) (2024)
- [A unified complexity bound for logconcave sampling](https://mlsanity.com/paper/2606.12694/) (2026)
- [Self-Concordant Perturbations for Linear Bandits](https://mlsanity.com/paper/2510.24187/) (2025)
- [Decomposable Non-Smooth Convex Optimization with Nearly-Linear Gradient Oracle Complexity](https://mlsanity.com/paper/2208.03811/) (2022)

## Abstract (arXiv)

For any convex body K subseteq mathbb Rn, S. Bubeck and R. Eldan introduced the entropic barrier on K and showed that it is a (1+o(1)) , n-self-concordant barrier. In this note, we observe that the optimal bound of n on the self-concordance parameter holds as a consequence of the dimensional Brascamp-Lieb inequality.