arXiv:2606. 29593v1 Announce Type: cross Abstract: In 1937, Stefan Kaczmarz proposed a simple algorithm for solving systems of linear equations.
arXiv:2509. 14969v2 Announce Type: replace Abstract: We introduce a new adaptive step-size strategy for convex optimization with stochastic gradient that exploits the local geometry of the objective function only by means of a first-order stochastic oracle and without any hyper-parameter tuning.
UCLA Professor Ernest Ryu and GPT-5 solved a key question in optimization theory, showcasing AI’s role in accelerating mathematical discovery.
A step-by-step journey from calculus-based optimization to Stochastic Gradient Descent The post Why Gradient Descent Became Stochastic appeared first on Towards Data Science .
arXiv:2608. 04607v1 Announce Type: cross Abstract: Stochastic gradient descent (SGD) optimization methods are the standard instruments for the training of deep neural networks (DNNs).
arXiv:2601. 16510v3 Announce Type: replace-cross Abstract: Solving massive-scale optimization problems requires scalable first-order methods with low per-iteration cost.
arXiv:2606. 01787v1 Announce Type: new Abstract: A new class of asynchronous adaptive first-order optimization methods is introduced, comprising asynchronous variants of several popular algorithms.
arXiv:2608. 10418v1 Announce Type: cross Abstract: Recent work has shown that, for smooth convex optimization, plain gradient descent can be accelerated from its textbook convergence rate of $O(T^{-1})$ (where $T$ denotes the number of iterations) to $O\big(T^{-\log_2(1+\sqrt{2})}\big)$ using carefully designed stepsize schedules alone, without resorting to momentum or other algorithmic modifications.
arXiv:2602. 05657v2 Announce Type: replace Abstract: The study of tail behaviour of SGD-induced processes has been attracting a lot of interest, due to offering strong guarantees with respect to individual runs of an algorithm.
arXiv:2606. 07496v1 Announce Type: new Abstract: Decentralized stochastic optimization is a fundamental paradigm for large-scale learning over networks, where agents communicate only with their neighbors and no central coordinator is required.
arXiv:2608. 16760v1 Announce Type: new Abstract: Reliable optimization is central to neural network (NN) training, yet Adam, the default optimizer for modern LLMs, rests on a fragile foundation.
arXiv:2301. 06308v2 Announce Type: replace-cross Abstract: Sharpness-aware minimization (SAM) is a training method that seeks to find flat minima in deep learning, resulting in state-of-the-art performance across various domains.
arXiv:2606. 24879v1 Announce Type: cross Abstract: We study the last iterate of the stochastic subgradient method for one-dimensional convex Lipschitz objectives.