The paper introduces an online sketched Newton method that uses a generalized accelerated sketch-and-project solver (GAS) to approximate Newton directions efficiently. GAS incorporates Nesterov momentum and a flexible projection metric, achieving accelerated convergence and reduced computational cost. The authors prove asymptotic normality and a functional central limit theorem for the averaged iterates, enabling an online inference procedure via random scaling that yields a pivotal test statistic with a parameter‑free limiting distribution.
arXiv:2508. 21022v3 Announce Type: replace Abstract: Subsampled natural gradient descent (SNG) has been used to enable high-precision scientific machine learning, but standard analyses based on stochastic preconditioning fail to provide insight into realistic small-sample settings.
arXiv:2609. 08136v1 Announce Type: new Abstract: This paper introduces rlaopt, a PyTorch-based package for large-scale optimization and scientific computing using randomized numerical linear algebra (RandNLA).
arXiv:2508.16791v2 Announce Type: replace-cross Abstract: We develop a novel past-extragradient-type algorithmic framework, combining both Nesterov's \textit{acceleration} and \textit{variance-reduct...
arXiv:2609.39595v1 Announce Type: new Abstract: Practical Muon maintains momentum and performs a small, fixed number of Newton--Schulz iterations separately for each parameter matrix, often with a Ne...
arXiv:2609.15723v1 Announce Type: new Abstract: Traditional variance reduction methods (e.g., SPIDER, SARAH, STORM) have been extensively investigated for improving the convergence rates of stochasti...
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:2608. 12665v1 Announce Type: cross Abstract: For solving nonconvex equality-constrained optimization problems, a recent Gradient-Eigenstep Algorithm by Goyens et al.
arXiv:2602. 20376v3 Announce Type: replace-cross Abstract: We study the problem of maximizing a complex-valued quadratic form over the $K^{\text{th}}$ roots of unity.
arXiv:2608. 21359v1 Announce Type: cross Abstract: We develop a new direct accelerated Newton method for minimizing convex functions with Lipschitz continuous Hessian.
arXiv:2606. 23867v1 Announce Type: new Abstract: The exact computation of the Normalized Maximum Likelihood (NML) codelength for regular non-smooth estimators (e.
arXiv:2607. 23008v1 Announce Type: cross Abstract: Optimization over probability measures has become an increasingly important paradigm in modern machine learning, scientific computing, and uncertainty quantification.
arXiv:2607. 28036v1 Announce Type: new Abstract: It is well known that Newton's method converges faster when the initial guess is closer to a root of a system of nonlinear equations.