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
Sep 23
Polyak-Type Extragradient Methods for Monotone Root-Finding Problems
The paper investigates Polyak-type step-size strategies for extragradient methods applied to deterministic and stochastic monotone root-finding problems. It shows that the projection-based correction in deterministic extragradient can be derived by minimizing an upper bound on the distance to a solution, mirroring classical Polyak step-size construction. The authors provide a unified deterministic analysis that does not require global Lipschitz continuity, achieving sublinear convergence under H"older or “(L0, L1)-Lipschitz” conditions and linear convergence with strong monotonicity, and extend the approach to stochastic settings with both direct and decreasing step-size variants.
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
4d ago
High-Probability Convergence of Clipped SGD under Heavy-Tailed Noise and $(L_0,L_1)$-Smoothness
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 Statistics ML
Aug 26
Lions and Muons: Optimization via Stochastic Frank-Wolfe under Heavy-Tailed Noise
arXiv:2506.04192v4 Announce Type: replace-cross Abstract: Stochastic Frank-Wolfe is a classical optimization method for solving constrained optimization problems. On the other hand, recent optimizers...
arXiv Computer Vision
Aug 26
Adaptive Extrapolated Proximal Gradient Methods with Variance Reduction for Composite Nonconvex Finite-Sum Minimization
arXiv:2502.21099v3 Announce Type: replace-cross Abstract: This paper proposes {\sf AEPG-SPIDER}, an Adaptive Extrapolated Proximal Gradient (AEPG) method with variance reduction for minimizing compos...
arXiv Statistics ML
4d ago
A stochastic subgradient method with optimal failure exponent
arXiv:2609.37425v1 Announce Type: cross Abstract: Fix a target accuracy $\varepsilon$, a gradient-noise level $s$, and a horizon $N$. We wish to design algorithms which minimize the probability of ob...
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
Sep 22
Accelerated stochastic first-order method for convex optimization under heavy-tailed noise
arXiv:2510.11676v2 Announce Type: replace-cross Abstract: We study convex composite optimization problems, where the objective function is given by the sum of a prox-friendly function and a convex fu...
Hugging Face Trending Papers
Aug 24
SGHA: A Single-Loop Fully First-Order Algorithm for Nonconvex-Strongly-Convex Bilevel Optimization
In this work, we study the oracle complexity of finding an $ε$-stationary point for nonconvex-strongly-convex (NC-SC) bilevel optimization using only first-order oracles. Existing methods achieving th...