# Exponential inequalities for nonstationary Markov Chains

arXiv: https://arxiv.org/abs/1808.08811 · HTML: https://mlsanity.com/paper/1808.08811/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 27 Aug 2018.

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

- [Testing Stationarity and Change Point Detection in Reinforcement Learning](https://mlsanity.com/paper/2203.01707/) (2022)
- [Deviation inequalities for stochastic approximation by averaging](https://mlsanity.com/paper/2102.08685/) (2021)
- [Rademacher learning rates for iterated random functions](https://mlsanity.com/paper/2506.13946/) (2025)

## Abstract (arXiv)

Exponential inequalities are main tools in machine learning theory. To prove exponential inequalities for non i.i.d random variables allows to extend many learning techniques to these variables. Indeed, much work has been done both on inequalities and learning theory for time series, in the past 15 years. However, for the non independent case, almost all the results concern stationary time series. This excludes many important applications: for example any series with a periodic behavior is non-stationary. In this paper, we extend the basic tools of Dedecker and Fan (2015) to nonstationary Markov chains. As an application, we provide a Bernstein-type inequality, and we deduce risk bounds for the prediction of periodic autoregressive processes with an unknown period.