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.
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