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In this paper, we obtain the Berry-Esseen bound for multivariate normal approximation for the Polyak-Ruppert averaged iterates of the linear stochastic approximation (LSA) algorithm with decreasing step size. Moreover, we prove the…

Machine Learning · Statistics 2025-02-04 Sergey Samsonov , Eric Moulines , Qi-Man Shao , Zhuo-Song Zhang , Alexey Naumov

In this paper, we refine the Berry-Esseen bounds for the multivariate normal approximation of Polyak-Ruppert averaged iterates arising from the linear stochastic approximation (LSA) algorithm with decreasing step size. We consider the…

Machine Learning · Statistics 2025-10-15 Bogdan Butyrin , Eric Moulines , Alexey Naumov , Sergey Samsonov , Qi-Man Shao , Zhuo-Song Zhang

Federated Learning has gained traction in privacy-sensitive collaborative environments, with local SGD emerging as a key optimization method in decentralized settings. While its convergence properties are well-studied, asymptotic…

Machine Learning · Statistics 2026-05-08 Soham Bonnerjee , Sayar Karmakar , Wei Biao Wu

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 $\mathcal{O}(n^{-1/4})$ convergence…

Machine Learning · Statistics 2025-05-27 Sergey Samsonov , Marina Sheshukova , Eric Moulines , Alexey Naumov

We study accuracy of bootstrap procedures for estimation of quantiles of a smooth function of a sum of independent sub-Gaussian random vectors. We establish higher-order approximation bounds with error terms depending on a sample size and a…

Statistics Theory · Mathematics 2020-09-21 Mayya Zhilova

This paper provides a non-asymptotic analysis of linear stochastic approximation (LSA) algorithms with fixed stepsize. This family of methods arises in many machine learning tasks and is used to obtain approximate solutions of a linear…

Machine Learning · Statistics 2021-06-03 Alain Durmus , Eric Moulines , Alexey Naumov , Sergey Samsonov , Kevin Scaman , Hoi-To Wai

Stochastic approximation with multiple coupled sequences (MSA) has found broad applications in machine learning as it encompasses a rich class of problems including bilevel optimization (BLO), multi-level compositional optimization (MCO),…

Machine Learning · Computer Science 2023-06-05 Davoud Ataee Tarzanagh , Mingchen Li , Pranay Sharma , Samet Oymak

In this paper we develop non-asymptotic Gaussian approximation results for the sampling distribution of suprema of empirical processes when the indexing function class $\mathcal{F}_n$ varies with the sample size $n$ and may not be Donsker.…

Statistics Theory · Mathematics 2023-09-06 Alexander Giessing

In this paper, we establish the non-asymptotic validity of the multiplier bootstrap procedure for constructing the confidence sets using the Stochastic Gradient Descent (SGD) algorithm. Under appropriate regularity conditions, our approach…

Non-asymptotic bounds for Gaussian and bootstrap approximation have recently attracted significant interest in high-dimensional statistics. This paper studies Berry-Esseen bounds for such approximations with respect to the multivariate…

Statistics Theory · Mathematics 2022-02-08 Miles E. Lopes

We study maximum likelihood estimation for spatial generalized linear mixed models with Gaussian process approximations using a stochastic Newton-Raphson algorithm. We consider two Gaussian Process approximations in this context: spectral…

Methodology · Statistics 2026-05-19 Samuel I. Watson , Yixin Wang , Emanuele Giorgi

This paper provides a finite-time analysis of linear stochastic approximation (LSA) algorithms with fixed step size, a core method in statistics and machine learning. LSA is used to compute approximate solutions of a $d$-dimensional linear…

Machine Learning · Statistics 2023-03-30 Alain Durmus , Eric Moulines , Alexey Naumov , Sergey Samsonov

Constant-stepsize stochastic approximation (SA) is widely used in learning for computational efficiency. For a fixed stepsize, the iterates typically admit a stationary distribution that is rarely tractable. Prior work shows that as the…

Machine Learning · Computer Science 2026-02-17 Zedong Wang , Yuyang Wang , Ijay Narang , Felix Wang , Yuzhou Wang , Siva Theja Maguluri

Federated learning faces critical challenges in balancing communication efficiency and model accuracy. One key issue lies in the approximation of update errors without incurring high computational costs. In this paper, we propose a…

Machine Learning · Computer Science 2025-05-29 Ganglou Xu

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…

Machine Learning · Statistics 2025-12-10 Bogdan Butyrin , Artemy Rubtsov , Alexey Naumov , Vladimir Ulyanov , Sergey Samsonov

Stochastic approximation (SA) is a powerful and scalable computational method for iteratively estimating the solution of optimization problems in the presence of randomness, particularly well-suited for large-scale and streaming data…

Statistics Theory · Mathematics 2023-10-03 Meimei Liu , Zuofeng Shang , Yun Yang

In this paper, we analyze the sample and communication complexity of the federated linear stochastic approximation (FedLSA) algorithm. We explicitly quantify the effects of local training with agent heterogeneity. We show that the…

Machine Learning · Statistics 2025-12-22 Paul Mangold , Sergey Samsonov , Safwan Labbi , Ilya Levin , Reda Alami , Alexey Naumov , Eric Moulines

We present a novel theoretical analysis of Federated SARSA (FedSARSA) with linear function approximation and local training. We establish convergence guarantees for FedSARSA in the presence of heterogeneity, both in local transitions and…

Machine Learning · Computer Science 2026-02-05 Paul Mangold , Eloïse Berthier , Eric Moulines

The classical line search for learning rate (LR) tuning in the stochastic gradient descent (SGD) algorithm can tame the convergence slowdown due to data-sampling noise. In a federated setting, wherein the client heterogeneity introduces a…

Machine Learning · Computer Science 2025-10-28 Geetika , Somya Tyagi , Bapi Chatterjee

This paper considers the Federated learning (FL) in a stochastic approximation (SA) framework. Here, each client $i$ trains a local model using its dataset $\mathcal{D}^{(i)}$ and periodically transmits the model parameters $w^{(i)}_n$ to a…

Machine Learning · Computer Science 2025-11-27 Srihari P , Anik Kumar Paul , Bharath Bhikkaji
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