# Deviation inequalities for stochastic approximation by averaging

arXiv: https://arxiv.org/abs/2102.08685 · HTML: https://mlsanity.com/paper/2102.08685/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 2 of its 26 references that are in the map.
- First posted on arXiv 17 Feb 2021.

## Builds on (most cited first, 2 of 2)

- [High dimensional VAR with low rank transition](https://mlsanity.com/paper/1905.00959/) (2019)
- [Exponential inequalities for nonstationary Markov Chains](https://mlsanity.com/paper/1808.08811/) (2018)

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

- [Minimax estimation of the pseudo-spectral gap of continuous Markov chains, with applications to empirical concentration bounds](https://mlsanity.com/paper/2610.20007/) (2026)

## Abstract (arXiv)

We introduce a class of Markov chains, that contains the model of stochastic approximation by averaging and non-averaging. Using martingale approximation method, we establish various deviation inequalities for separately Lipschitz functions of such a chain, with different moment conditions on some dominating random variables of martingale differences.Finally, we apply these inequalities to the stochastic approximation by averaging and empirical risk minimisation.