%0 Journal Article
%T Sharp Finite-Time Iterated-Logarithm Martingale Concentration
%A Akshay Balsubramani
%J Computer Science
%D 2014
%I arXiv
%X 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.
%U http://arxiv.org/abs/1405.2639v4