Statistical inference for Linear Stochastic Approximation with Markovian Noise

S. Samsonov; M. Sheshukova; Moulines E.; A. Naumov

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Statistical inference for Linear Stochastic Approximation with Markovian Noise

P. 174565–174626.

Samsonov S., Sheshukova M., Moulines E., Naumov A.

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 nonasymptotic 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.

Language: English

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Keywords: Markovian noise linear stochastic approximation

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39th Conference on Neural Information Processing Systems (NeurIPS 2025)

NeurIPS, 2025.

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