mlsanityData to 7 Oct 2026

The entropic barrier: a simple and optimal universal self-concordant barrier

arXiv 1412.1587 ↗First posted 4 Dec 2014math.OC cs.IT cs.LGcited by 15

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Abstract (arXiv)

We prove that the Cram'er transform of the uniform measure on a convex body in ℝn is a (1+o(1)) n-self-concordant barrier, improving a seminal result of Nesterov and Nemirovski. This gives the first explicit construction of a universal barrier for convex bodies with optimal self-concordance parameter. The proof is based on basic geometry of log-concave distributions, and elementary duality in exponential families.

Key facts. Cited by 15 papers in the map (data through 7 Oct 2026). First posted on arXiv 4 Dec 2014.

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Citing papers per year: 2021: 2; 2022: 3; 2023: 3; 2024: 1; 2025: 2; 2026: 4.

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  1. 2023Mirror Diffusion Models for Constrained and Watermarked Generationcited by 38
  2. 2023A Unified Analysis of Nonstochastic Delayed Feedback for Combinatorial Semi-Bandits, Linear Bandits, and MDPscited by 15
  3. 2023Banker Online Mirror Descent: A Universal Approach for Delayed Online Bandit Learningcited by 7
  4. 2021Optimization and Sampling Under Continuous Symmetry: Examples and Lie Theorycited by 5
  5. 2022Contextual Pandora's Boxcited by 5
  6. 2025An Improved Algorithm for Adversarial Linear Contextual Bandits via Reductioncited by 3
  7. 2026Swap Regret Minimization Through Response-Based Approachabilitycited by 2
  8. 2022Sampling from Log-Concave Distributions over Polytopes via a Soft-Threshold Dikin Walkcited by 1
  9. 2026Beyond the d2.5-mixing bound for Dikin walks on polytopescited by 1
  10. 2021Convergence Rates for the MAP of an Exponential Family and Stochastic Mirror Descent -- an Open Problemcited by 0
  11. 2022Decomposable Non-Smooth Convex Optimization with Nearly-Linear Gradient Oracle Complexitycited by 0
  12. 2024A conversion theorem and minimax optimality for continuum contextual banditscited by 0
3 more
  1. 2025Self-Concordant Perturbations for Linear Banditscited by 0
  2. 2026Pliable rejection samplingcited by 0
  3. 2026A Complete Characterization of Learnability for Adversarial Noisy Banditscited by 0