arXiv:2609.06064v1 Announce Type: cross Abstract: Stochastic min-max optimization has attracted increasing attention due to its applications in modern machine learning, while existing theoretical stu...
arXiv:2609.24423v1 Announce Type: cross Abstract: We consider a standard convex composite optimization problem with either smooth or nonsmooth objective function, and under quadratic growth. In recen...
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: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:2511. 19656v3 Announce Type: replace Abstract: Although upper bound guarantees for bilevel optimization have been widely studied, progress on lower bounds has been limited due to the complexity of the bilevel structure.
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:2609.08380v1 Announce Type: cross Abstract: We study the stochastic first-order oracle complexity for constrained or regularized convex-concave min-max optimization and stochastic monotone vari...
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.
The paper proves that stochastic gradient descent with gradient clipping and additive Gaussian noise (SGD‑CN) converges almost surely under smoothness and bounded noise assumptions, given standard decaying step sizes. The analysis extends to momentum variants such as the stochastic heavy ball and Nesterov's accelerated gradient, showing that careful energy constructions yield similar guarantees. These results provide stronger theoretical foundations for understanding the pathwise behaviour of clipped stochastic gradient methods in both convex and nonconvex regimes.
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:2607. 06883v1 Announce Type: cross Abstract: We consider the problem of finding stationary points for stochastic convex optimization problems.
arXiv:2609.15679v1 Announce Type: cross Abstract: This paper studies projection-free algorithms for stochastic constrained multi-level compositional optimization. In this context, the objective funct...