This paper studies the statistical properties of Stochastic Gradient Descent (SGD) with a constant step size using the framework of iterated random functions. It demonstrates convergence in Euclidean distance via Geometric Moment Contraction, establishes quenched central limit theorems, invariance principles, and α-stable convergence for averaged SGD regardless of initialization, and explores the effect of step sizes through derivative processes. The authors further develop a Richardson-Romberg extrapolation with multiple step sizes, propose a bias-reduced variant, and introduce an online inference method that yields empirical confidence intervals with coverage approaching nominal levels as sample size increases.
By Jiaqi Li, Zhipeng Lou, Stefan Richter, Wei Biao Wu
arXiv:2602.13960v2 Announce Type: replace
Abstract: Constant-stepsize stochastic approximation (SA) is widely used in learning for computational efficiency, yet the distribution of the iterates is ty...
By Zedong Wang, Yuyang Wang, Ijay Narang, Felix Wang, Yuzhou Wang, Siva Theja Maguluri
arXiv:2602. 13906v2 Announce Type: replace-cross Abstract: Stochastic approximation (SA) is a method for finding the root of an operator perturbed by noise.
By Shaan Ul Haque, Zedong Wang, Zixuan Zhang, Siva Theja Maguluri
arXiv:2605. 26000v2 Announce Type: replace-cross Abstract: Stochastic gradient descent (SGD) is foundational to large-scale statistical learning and stochastic optimization.
By Jose Blanchet, Peter Glynn, Wenhao Yang
arXiv:2609.14922v1 Announce Type: cross
Abstract: For constant-stepsize stochastic approximation (SA), the iterates converge in distribution to a stationary law that depends on the stepsize $\alpha.$...
By Yixuan Zhang, Qiaomin Xie
arXiv:2608. 25551v1 Announce Type: new Abstract: Stochastic gradient descent (SGD) is typically analyzed at a deterministic horizon chosen before the algorithm is run, even though practical stopping decisions are made adaptively by inspecting the evolving trajectory.
By Liviu Aolaritei, Lucas L\'evy, Francis Bach, Michael I. Jordan
arXiv:2505.20817v3 Announce Type: replace-cross
Abstract: Gradient clipping is widely used in language-model training to control heavy-tailed gradient noise and can improve convergence guarantees ove...
By Taha El Bakkali El Kadi, Savelii Chezhegov, Aleksandr Beznosikov, Samuel Horv\'ath, Eduard Gorbunov
The paper introduces Fast Regularized Policy Mirror Descent (PMD) that pairs policy updates with a single temporal-difference (TD) critic step. It proves global linear convergence for finite discounted MDPs using exact coordinate-wise Bellman updates and any positive actor stepsize, regardless of critic initialization. For stochastic TD-PMD with strongly convex mirror maps, the authors achieve an expected value gap of ε after “~O(1/((1-γ)^5 σ_b ε))” transitions, without requiring trajectory resets, generative models, or nested policy evaluation loops.
By Qipei Chen, Wenye Li, Yule Sun, Ke Wei
arXiv:2606. 05967v1 Announce Type: cross Abstract: In this paper, we study the finite-time behavior of the TD(0) temporal-difference method with linear function approximation (LFA).
By Ziad Kobeissi (L2S), \'Elo\"ise Berthier (U2IS)
arXiv:2502. 09884v4 Announce Type: replace-cross Abstract: We consider linear two-time-scale stochastic approximation algorithms driven by martingale noise.
By Seo Taek Kong, Sihan Zeng, Thinh T. Doan, R. Srikant
arXiv:2609. 29961v1 Announce Type: new Abstract: Many iterative algorithms rely on bootstrapping.
By Ids van der Werf, Sergio Rozada, Antonio G. Marques
arXiv:2608. 05460v1 Announce Type: cross Abstract: This work introduces a proximal stochastic subgradient method for minimizing the sum of an expected cost, whose integrand is potentially nonsmooth and nonconvex, and a lower semicontinuous, prox-bounded function.
By Felipe Atenas, Alejandro Jofr\'e, Pedro P\'erez-Aros, David Torregrosa-Bel\'en