# PAC-Bayes Iterated Logarithm Bounds for Martingale Mixtures

arXiv: https://arxiv.org/abs/1506.06573 · HTML: https://mlsanity.com/paper/1506.06573/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 22 Jun 2015.

## Built on by (most cited first, 3 of 3)

- [A unified recipe for deriving (time-uniform) PAC-Bayes bounds](https://mlsanity.com/paper/2302.03421/) (2023)
- [PAC-Bayes Bounds for Bandit Problems: A Survey and Experimental Comparison](https://mlsanity.com/paper/2211.16110/) (2022)
- [PAC-Bayesian Lifelong Learning For Multi-Armed Bandits](https://mlsanity.com/paper/2203.03303/) (2022)

## Abstract (arXiv)

We give tight concentration bounds for mixtures of martingales that are simultaneously uniform over (a) mixture distributions, in a PAC-Bayes sense; and (b) all finite times. These bounds are proved in terms of the martingale variance, extending classical Bernstein inequalities, and sharpening and simplifying prior work.