# A note on concentration inequality for vector-valued martingales with weak exponential-type tails

arXiv: https://arxiv.org/abs/1809.02495 · HTML: https://mlsanity.com/paper/1809.02495/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 6 Sep 2018.

## Built on by (most cited first, 1 of 1)

- [Mirror Natural Evolution Strategies](https://mlsanity.com/paper/2308.00469/) (2023)

## Abstract (arXiv)

We present novel martingale concentration inequalities for martingale differences with finite Orlicz-psiα norms. Such martingale differences with weak exponential-type tails scatters in many statistical applications and can be heavier than sub-exponential distributions. In the case of one dimension, we prove in general that for a sequence of scalar-valued supermartingale difference, the tail bound depends solely on the sum of squared Orlicz-psiα norms instead of the maximal Orlicz-psiα norm, generalizing the results of Lesigne & Voln'y (2001) and Fan et al. (2012). In the multidimensional case, using a dimension reduction lemma proposed by Kallenberg & Sztencel (1991) we show that essentially the same concentration tail bound holds for vector-valued martingale difference sequences.