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Stochastic approximation is a framework unifying many random iterative algorithms occurring in a diverse range of applications. The stability of the process is often difficult to verify in practical applications and the process may even be…

Probability · Mathematics 2014-03-10 Christophe Andrieu , Matti Vihola

We study the so-called two-time-scale stochastic approximation, a simulation-based approach for finding the roots of two coupled nonlinear operators. Our focus is to characterize its finite-time performance in a Markov setting, which often…

Optimization and Control · Mathematics 2021-04-06 Thinh T. Doan

Stochastic approximation (SA) with multiple coupled sequences has found broad applications in machine learning such as bilevel learning and reinforcement learning (RL). In this paper, we study the finite-time convergence of nonlinear SA…

Machine Learning · Computer Science 2022-06-22 Han Shen , Tianyi Chen

Two-time-scale Stochastic Approximation (SA) is an iterative algorithm with applications in reinforcement learning and optimization. Prior finite time analysis of such algorithms has focused on fixed point iterations with mappings…

Machine Learning · Computer Science 2025-09-30 Siddharth Chandak , Shaan Ul Haque , Nicholas Bambos

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

Stochastic approximation (SA) is a fundamental iterative framework with broad applications in reinforcement learning and optimization. Classical analyses typically rely on martingale difference or Markov noise with bounded second moments,…

Machine Learning · Computer Science 2026-03-23 Siddharth Chandak , Anuj Yadav , Ayfer Ozgur , Nicholas Bambos

Stochastic approximation is a class of algorithms that update a vector iteratively, incrementally, and stochastically, including, e.g., stochastic gradient descent and temporal difference learning. One fundamental challenge in analyzing a…

Machine Learning · Computer Science 2025-11-06 Shuze Daniel Liu , Shuhang Chen , Shangtong Zhang

Stochastic approximation (SA) is a key method used in statistical learning. Recently, its non-asymptotic convergence analysis has been considered in many papers. However, most of the prior analyses are made under restrictive assumptions…

Machine Learning · Statistics 2019-06-18 Belhal Karimi , Blazej Miasojedow , Eric Moulines , Hoi-To Wai

Motivated by Q-learning, we study nonsmooth contractive stochastic approximation (SA) with constant stepsize. We focus on two important classes of dynamics: 1) nonsmooth contractive SA with additive noise, and 2) synchronous and…

Machine Learning · Statistics 2024-04-25 Yixuan Zhang , Dongyan Huo , Yudong Chen , Qiaomin Xie

This paper considers a novel multi-agent linear stochastic approximation algorithm driven by Markovian noise and general consensus-type interaction, in which each agent evolves according to its local stochastic approximation process which…

Machine Learning · Computer Science 2023-10-02 Yixuan Lin , Vijay Gupta , Ji Liu

Motivated by engineering applications such as resource allocation in networks and inventory systems, we consider average-reward Reinforcement Learning with unbounded state space and reward function. Recent works studied this problem in the…

Machine Learning · Computer Science 2025-11-10 Shaan Ul Haque , Siva Theja Maguluri

Asynchronous stochastic approximations (SAs) are an important class of model-free algorithms, tools and techniques that are popular in multi-agent and distributed control scenarios. To counter Bellman's curse of dimensionality, such…

Optimization and Control · Mathematics 2019-05-03 Arunselvan Ramaswamy , Shalabh Bhatnagar , Daniel E. Quevedo

Stochastic Approximation (SA) is a classical algorithm that has had since the early days a huge impact on signal processing, and nowadays on machine learning, due to the necessity to deal with a large amount of data observed with…

Optimization and Control · Mathematics 2023-07-18 Aymeric Dieuleveut , Gersende Fort , Eric Moulines , Hoi-To Wai

We study stochastic approximation procedures for approximately solving a $d$-dimensional linear fixed point equation based on observing a trajectory of length $n$ from an ergodic Markov chain. We first exhibit a non-asymptotic bound of the…

Optimization and Control · Mathematics 2024-05-14 Wenlong Mou , Ashwin Pananjady , Martin J. Wainwright , Peter L. Bartlett

This paper presents the first sufficient conditions that guarantee the stability and almost sure convergence of multi-timescale stochastic approximation (SA) iterates. It extends the existing results on one-timescale and two-timescale SA…

Systems and Control · Electrical Eng. & Systems 2025-10-16 Rohan Deb , Swetha Ganesh , Shalabh Bhatnagar

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

In this paper, we study the effectiveness of using a constant stepsize in statistical inference via linear stochastic approximation (LSA) algorithms with Markovian data. After establishing a Central Limit Theorem (CLT), we outline an…

Machine Learning · Statistics 2023-12-19 Dongyan Huo , Yudong Chen , Qiaomin Xie

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

We generalize the Borkar-Meyn stability Theorem (BMT) to distributed stochastic approximations (SAs) with information delays that possess an arbitrary moment bound. To model the delays, we introduce Age of Information Processes (AoIPs):…

Optimization and Control · Mathematics 2023-05-15 Adrian Redder , Arunselvan Ramaswamy , Holger Karl

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