arXiv:2608. 01552v1 Announce Type: cross Abstract: Quadratic Gradient (QG) is a Newton-type optimization framework that bridges first-order gradient descent and second-order optimization by incorporating curvature information into gradient updates.
By John Chiang
arXiv:2508. 00775v2 Announce Type: replace-cross Abstract: The design of many classical optimization algorithms is driven by the certification of linear convergence rates over classes of optimization problems.
By Andrea Martin, Ian R. Manchester, Luca Furieri
arXiv:2406. 14340v2 Announce Type: replace-cross Abstract: The standard stochastic gradient descent (SGD) optimization method, as well as adaptive methods such as the Adam optimizer fail to converge if the learning rates do not converge to zero (particularly, in the situation of constant learning rates).
By Steffen Dereich, Arnulf Jentzen, Adrian Riekert
arXiv:2503. 04712v3 Announce Type: replace-cross Abstract: We study the optimization of non-convex functions that are not necessarily smooth (gradient and/or Hessian are Lipschitz) using first order methods.
By Daniel Yiming Cao, August Y. Chen, Karthik Sridharan, Benjamin Tang
arXiv:2608. 09523v1 Announce Type: new Abstract: Deep neural network (DNN) training with stochastic gradient descent (SGD) and its variants achieves strong empirical performance, yet classical optimization theory does not fully explain this success.
By Binchuan Qi
arXiv:2606. 16926v1 Announce Type: cross Abstract: Functional optimization problems are typically solved by optimizing the parameters of a fixed representation, such as a neural network, resulting in highly nonconvex losses that complicate both training and theoretical analysis.
By Daniel Csillag, Rodrigo Schuller, Pedro Dall'Antonia, Leonidas Guibas, Luiz Velho, Tiago Novello