arXiv Machine Learning
Jul 9
Finding a stationary point of a stochastic convex problem
arXiv:2607. 06883v1 Announce Type: cross Abstract: We consider the problem of finding stationary points for stochastic convex optimization problems.
A proximal subgradient method for nonconvex stochastic optimization under the Kurdyka-{\L}ojasiewicz condition
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.
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arXiv Machine Learning
Aug 7
On Same-Sample and Independent-Sample Stochastic Extragradient for Monotone Variational Inequalities
arXiv:2608. 06182v1 Announce Type: cross Abstract: We study stochastic extragradient (SEG) methods for solving monotone variational inequality problems (VIPs) over a feasible set.
arXiv Machine Learning
Jul 2
Towards Weaker Variance Assumptions for Stochastic Optimization
arXiv:2504. 09951v2 Announce Type: replace-cross Abstract: We revisit a classical assumption for analyzing stochastic gradient algorithms where the squared norm of the stochastic subgradient (or the variance for smooth problems) is allowed to grow as fast as the squared norm of the optimization variable.
arXiv Machine Learning
Aug 5
Stochastic Saddle Avoidance Beyond Unit Excitation and Smoothness: A Pathwise Lyapunov-Perron Framework
arXiv:2608. 03001v1 Announce Type: cross Abstract: Unit excitation (UE) is a common assumption in stochastic saddle avoidance: the stochastic error must have a uniformly positive component along every direction, in expectation.
arXiv Machine Learning
Jun 2
Can Adaptive Gradient Methods Converge under Heavy-Tailed Noise? A Case Study of AdaGrad
arXiv:2605. 18694v2 Announce Type: replace-cross Abstract: Many tasks in modern machine learning are observed to involve heavy-tailed gradient noise during the optimization process.
arXiv Machine Learning
Jul 13
Solving Stochastic Fixed-Point Equations with High Probability
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 Machine Learning
Jun 24
New Bounds for the Last Iterate of the Stochastic subGradient Method
arXiv:2606. 24879v1 Announce Type: cross Abstract: We study the last iterate of the stochastic subgradient method for one-dimensional convex Lipschitz objectives.
arXiv Machine Learning
6d ago
Adaptive Bregman Proximal Stochastic Gradient with a Stabilized Barzilai--Borwein Step Size
arXiv:2608. 12009v1 Announce Type: cross Abstract: Bregman proximal stochastic gradient (BPSG) methods bring variance-reduced composite optimization to objectives whose geometry is poorly captured by Euclidean smoothness.
arXiv Machine Learning
Jun 2
In-Expectation Convergence of Stochastic Gradient Methods under Heavy-Tailed Noise
arXiv:2606. 00520v1 Announce Type: cross Abstract: Many stochastic gradient methods are believed not to converge when the noise in stochastic gradients has only a finite $p$-th moment for $p\in\left(1,2\right)$, a setting known as the heavy-tailed noise assumption.
arXiv Machine Learning
Aug 10
Mean-square and sublinear convergence of a stochastic proximal point algorithm in metric spaces of nonpositive curvature
arXiv:2510. 10697v2 Announce Type: replace-cross Abstract: We define a stochastic variant of the proximal point algorithm in the general setting of nonlinear Hadamard spaces for approximating zeros of the mean of a stochastically perturbed monotone vector field.
Hugging Face Trending Papers
Aug 4
Stochastic Saddle Avoidance Beyond Unit Excitation and Smoothness: A Pathwise Lyapunov-Perron Framework
Unit excitation (UE) is a common assumption in stochastic saddle avoidance: the stochastic error must have a uniformly positive component along every direction, in expectation. This condition gives a direct way to rule out convergence to strict saddles, but it also oversimplifies the actual noise structure, and does not match many stochastic optimization regimes.
arXiv Machine Learning
Jun 24
Accelerated Stochastic Min-Max Optimization Based on Bias-corrected Momentum
arXiv:2406. 13041v3 Announce Type: replace Abstract: Lower-bound analyses for nonconvex strongly-concave minimax optimization problems have shown that stochastic first-order algorithms require at least $\mathcal{O}(\varepsilon^{-4})$ sample complexity to find an $\varepsilon$-stationary point.