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:2606. 24879v1 Announce Type: cross Abstract: We study the last iterate of the stochastic subgradient method for one-dimensional convex Lipschitz objectives.
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.
arXiv:2607. 06883v1 Announce Type: cross Abstract: We consider the problem of finding stationary points for stochastic convex optimization problems.
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:2606. 21528v2 Announce Type: replace-cross Abstract: We study first-order methods for solving monotone variational inequalities arising in min-max optimization.
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.
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: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: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: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.
arXiv:2607. 14731v1 Announce Type: new Abstract: Local SGD, also known as Federated Averaging, is a widely used distributed optimization algorithm.
arXiv:2512. 02342v3 Announce Type: replace-cross Abstract: The stochastic Polyak step size (SPS) has proven to be a promising choice for stochastic gradient descent (SGD), delivering competitive performance relative to state-of-the-art methods on smooth convex and non-convex optimization problems, including deep neural network training.