arXiv:2607. 08104v1 Announce Type: new Abstract: Stochastic gradient descent (SGD) is a cornerstone of modern optimization.
By Ryusei Yamada, Naoki Sato, Hideaki Iiduka
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.
By Dimitris Oikonomou, Nicolas Loizou
arXiv:2209. 03282v5 Announce Type: replace-cross Abstract: Accelerating the convergence of second-order optimization, particularly Newton-type methods, remains a pivotal challenge in algorithmic research.
By John Chiang
arXiv:2606. 12054v1 Announce Type: new Abstract: Injecting noise into the optimization process is a well-established technique for improving the training and generalization of deep neural networks.
By Benjamin Leblanc, Louis-Jacob Lebel, Teddy Kana, Richard Kamel
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.
By Amartya Mukherjee, Jun Liu
arXiv:2606. 07088v1 Announce Type: new Abstract: Stochastic constrained decision-making requires optimizing performance objectives while enforcing statistical requirements such as safety or fairness.
By Kang Liu, Jianchen Hu, Ziyu Qu