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Sharp Finite-Time Iterated-Logarithm Martingale Concentration

Probability 2015-12-03 v4 Machine Learning Machine Learning

Abstract

We give concentration bounds for martingales that are uniform over finite times and extend classical Hoeffding and Bernstein inequalities. We also demonstrate our concentration bounds to be optimal with a matching anti-concentration inequality, proved using the same method. Together these constitute a finite-time version of the law of the iterated logarithm, and shed light on the relationship between it and the central limit theorem.

Keywords

Cite

@article{arxiv.1405.2639,
  title  = {Sharp Finite-Time Iterated-Logarithm Martingale Concentration},
  author = {Akshay Balsubramani},
  journal= {arXiv preprint arXiv:1405.2639},
  year   = {2015}
}

Comments

25 pages

R2 v1 2026-06-22T04:11:28.255Z