In this paper we derive non-asymptotic Berry-Esseen bounds for Polyak-Ruppert averaged iterates of the Linear Stochastic Approximation (LSA) algorithm driven by the Markovian noise. Our analysis yields O(n−1/4) convergence rates to the Gaussian limit in the Kolmogorov distance. We further establish the non-asymptotic validity of a multiplier block bootstrap procedure for constructing the confidence intervals, guaranteeing consistent inference under Markovian sampling. Our work provides the first non-asymptotic guarantees on the rate of convergence of bootstrap-based confidence intervals for stochastic approximation with Markov noise. Moreover, we recover the classical rate of order O(n−1/8) up to logarithmic factors for estimating the asymptotic variance of the iterates of the LSA algorithm.
@article{arxiv.2505.19102,
title = {Statistical inference for Linear Stochastic Approximation with Markovian Noise},
author = {Sergey Samsonov and Marina Sheshukova and Eric Moulines and Alexey Naumov},
journal= {arXiv preprint arXiv:2505.19102},
year = {2025}
}