The entropic barrier is n-self-concordant

2021/12/21 by Sinho Chewi, Chewi, Sinho · 2 citations
Biochemistry, Genetics and Molecular Biology · Mathematics · #Diffusion and Search Dynamics #FOS: Computer and information sciences #FOS: Mathematics #Machine Learning (cs.LG) #Metric Geometry (math.MG) #Optimization and Control (math.OC) #Point processes and geometric inequalities

paper · pdf · doi:10.48550/arxiv.2112.10947

openalex publication_date 2021/12/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

For any convex body K ⊆ \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.

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