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: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:2602.13960v2 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...
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:2602. 13906v2 Announce Type: replace-cross Abstract: Stochastic approximation (SA) is a method for finding the root of an operator perturbed by noise.
arXiv:2606. 26316v1 Announce Type: new Abstract: We study first-order methods for smooth objectives satisfying the Polyak-\L{}ojasiewicz (PL) condition when gradient samples are generated by an exogenous Markov chain.
The paper establishes a shrinking‑tube concentration bound for projected stochastic approximation driven by an adaptive Markov chain, guaranteeing that after a chosen time every iterate stays within a tolerance that tightens over time. The bound’s probability of any exit after that time decays polynomially, and a matching lower bound shows this exponent is optimal under finite second moments. Extensions to recursions with martingale‑difference noise and predictable bias reveal how noise scale and bias affect exit‑probability decay and tube shrinkage, with applications to inventory learning and numerical gradient accuracy.
arXiv:2609. 29961v1 Announce Type: new Abstract: Many iterative algorithms rely on bootstrapping.
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:2609.40193v1 Announce Type: new Abstract: We establish near-linear accuracy bounds for the classical Moreau--Yosida unadjusted Langevin algorithm (MYULA). The target is $\pi\propto e^{-f-g}$, w...
arXiv:2606. 24879v1 Announce Type: cross Abstract: We study the last iterate of the stochastic subgradient method for one-dimensional convex Lipschitz objectives.
arXiv:2609.38880v1 Announce Type: new Abstract: We study the last iterate of standard tabular temporal-difference (TD) learning from a single trajectory of a finite Markov reward process. For discoun...
arXiv:2607. 07967v1 Announce Type: cross Abstract: Diffusion-based policies have recently emerged as powerful policy parameterizations for reinforcement learning, representing state-conditioned action distributions as terminal laws of diffusion processes with parameterized drifts.