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arXiv · 2508.07928

Gaussian Approximation for Two-Timescale Linear Stochastic Approximation

Bogdan Butyrin·Artemy Rubtsov·Alexey Naumov·Vladimir Ulyanov·Sergey Samsonov
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Abstract

In this paper, we establish non-asymptotic bounds for accuracy of normal approximation for linear two-timescale stochastic approximation (TTSA) algorithms driven by martingale difference or Markov noise. Focusing on both the last iterate and Polyak-Ruppert averaging regimes, we derive bounds for normal approximation in terms of the convex distance between probability distributions. Our analysis reveals a non-trivial interaction between the fast and slow timescales: the normal approximation rate for the last iterate improves as the timescale separation increases, while it decreases in the Polyak-Ruppert averaged setting. We also provide the high-order moment bounds for the error of linear TTSA algorithm, which may be of independent interest.

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BibTeXRIS

Bogdan Butyrin, Artemy Rubtsov, Alexey Naumov, Vladimir Ulyanov, Sergey Samsonov. 2025-08-11. Gaussian Approximation for Two-Timescale Linear Stochastic Approximation. https://arxiv.org/abs/2508.07928

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