arXiv:2609. 04578v1 Announce Type: cross Abstract: We study stochastic gradient descent with random reshuffling for finite sums \[ F(x)=\frac1n\sum_{i=1}^n f_i(x).
arXiv:2607. 16384v1 Announce Type: new Abstract: For stochastic gradient descent (SGD) with a constant stepsize $\alpha$, the invariant law of the iterates, centered at a minimizer, describes the behavior of the algorithm over long time horizons.
arXiv:2608. 13467v1 Announce Type: new Abstract: We study the Moreau--Yosida unadjusted Langevin algorithm (MYULA) for the nonsmooth composite target \[ \pi(dx)\propto \exp\{-f(x)-g(x)\}\,dx, \qquad x\in\mathbb R^d, \] where \(f\) is \(m\)-strongly convex with \(L_f\)-Lipschitz gradient and \(g\) is convex and \(G\)-Lipschitz.
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. 29458v1 Announce Type: new Abstract: We present a tightened convergence analysis of clipped gradient descent on $(L_0, L_1)$-smooth functions, with quantitative constants.
The paper introduces RanSOM, a second‑order momentum algorithm that eliminates the need for a Lipschitz Hessian or auxiliary forward/backward passes by randomizing the step length. By sampling the step from an exponential distribution and using a Stein‑type identity, the method obtains an unbiased estimate of the gradient change with a single Hessian‑vector product that also serves the next gradient computation. RanSOM-E achieves optimal oracle‑complexity exponents for heavy‑tailed noise without clipping, while RanSOM-B preserves feasibility for Frank‑Wolfe iterates, and experiments on CIFAR‑10 show comparable accuracy to existing methods with lower update time.
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.
arXiv:2605. 12461v2 Announce Type: replace-cross Abstract: We propose an algorithm to sample from composite log-concave distributions over $\mathbb{R}^d$, i.
arXiv:2606. 14488v1 Announce Type: cross Abstract: Recent finite-time analyses of nonlinear two-time-scale stochastic approximation show that under contractive assumptions the slow iterate $Y_k$ with stepsizes $\beta_k=\Theta(k^{-1})$ and $\alpha_k=\Theta(k^{-a})$, $a\in(1/2,1)$, generally satisfies a mean-square rate of order $k^{-a}$; decoupled $k^{-1}$ rates require strong local linearity.
arXiv:2310. 15976v4 Announce Type: replace Abstract: signSGD is attractive in nonconvex optimization because it communicates sign-valued rather than full-precision gradients.
arXiv:2609.31303v1 Announce Type: new Abstract: We study geometric moment contraction (GMC) of the constant-parameter stochastic Nesterov recursion \[ Y_k=\Theta_k+\beta(\Theta_k-\Theta_{k-1}),\qquad...
arXiv:2609. 21880v1 Announce Type: cross Abstract: We study the optimization of convex objectives with $(L,\kappa-1)$-H\"older-continuous gradients in $\ell_q$ over $R B_p^d$, $1<\kappa\le 2$.
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.