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 $\alpha.$...
arXiv:2602. 13906v2 Announce Type: replace-cross Abstract: Stochastic approximation (SA) is a method for finding the root of an operator perturbed by noise.
arXiv:2610. 14567v2 Announce Type: replace-cross Abstract: This paper develops strong Gaussian approximations (KMT type) for constant learning rate stochastic gradient descent (SGD).
arXiv:2609. 39144v2 Announce Type: new Abstract: We prove a sharp Gaussian approximation for the invariant law of constant-stepsize SGD with bounded additive noise generated by an exogenous uniformly ergodic Markov chain.
arXiv:2607. 09097v1 Announce Type: cross Abstract: We study stochastic fixed-point equations $\mathbf{T}(\mathbf{x}) = \mathbf{x}$ over normed spaces $(\mathcal{E}, \|\cdot\|)$, where the operator $\mathbf{T}$ is nonexpansive or contractive and is accessed only through unbiased stochastic evaluations with bounded second central moment.
arXiv:2607. 17595v1 Announce Type: new Abstract: We establish mean-square and concentration bounds for stochastic approximation (SA) with arbitrary norm contractive mappings, under a multiplicative noise model where the noise may scale affinely with the norm of the iterates, and the iterates are potentially unbounded.
arXiv:2502. 09884v4 Announce Type: replace-cross Abstract: We consider linear two-time-scale stochastic approximation algorithms driven by martingale noise.
arXiv:2609.37787v1 Announce Type: new Abstract: Adam is widely observed to remain stable even when the objective deviates significantly from global smoothness. Under the generalized smoothness framew...
arXiv:2602. 05657v2 Announce Type: replace Abstract: The study of tail behaviour of SGD-induced processes has been attracting a lot of interest, due to offering strong guarantees with respect to individual runs of an algorithm.
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.
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...
arXiv:2609. 12785v1 Announce Type: new Abstract: Classical convergence guarantees for stochastic gradient methods typically assume Lipschitz-smooth objectives and finite-variance gradient noise, both frequently violated in practice.