The paper investigates last‑iterate convergence for proximal and projected stochastic gradient methods in settings without bounded domain or bounded variance assumptions, using black‑box variational inference as an example. It establishes a near‑optimal anytime rate of ×(1/√T) for the last iterate under two relaxed assumptions, and shows that when the horizon T is known, the logarithmic factor can be removed to achieve the optimal ×(1/√T) rate, matching results that previously required bounded variance or domain constraints.
arXiv:2606. 24879v1 Announce Type: cross Abstract: We study the last iterate of the stochastic subgradient method for one-dimensional convex Lipschitz objectives.
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.
The paper establishes the first optimal last‑iterate convergence rates, in high probability, for Clipped‑SGD when the gradient noise is heavy‑tailed. It addresses the gap left by earlier results that required strong noise assumptions, such as exponentially decaying tails. By proving these rates, the authors provide theoretical support for the practical effectiveness of gradient clipping in stochastic convex optimization.
arXiv:2606. 21528v2 Announce Type: replace-cross Abstract: We study first-order methods for solving monotone variational inequalities arising in min-max optimization.
arXiv:2609.15257v1 Announce Type: cross Abstract: We analyze a stochastic algorithm with Halpern anchoring for constrained convex-concave problems and monotone variational inequalities. This algorith...
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:2604.13870v2 Announce Type: replace-cross Abstract: We consider the well-studied setting of minimizing a convex Lipschitz function using either gradient descent (GD) or its stochastic variant (...
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:2608. 25551v1 Announce Type: new Abstract: Stochastic gradient descent (SGD) is typically analyzed at a deterministic horizon chosen before the algorithm is run, even though practical stopping decisions are made adaptively by inspecting the evolving trajectory.
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:2609.30274v1 Announce Type: new Abstract: Machine Learning and more specifically Deep Learning involves solving large scale nonconvex optimization problems. Several algorithms have been propose...
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...