arXiv:2606. 06934v1 Announce Type: new Abstract: We analyze generalization error, uniform stability, and uniform argument stability of gradient descent (GD) and stochastic gradient descent (SGD) over discrete parameter spaces, where each update involves deterministic or stochastic rounding.
arXiv:2607. 14731v1 Announce Type: new Abstract: Local SGD, also known as Federated Averaging, is a widely used distributed optimization algorithm.
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. 14789v2 Announce Type: replace Abstract: The dynamical stability of the iterates during training plays a key role in determining the minima obtained by optimization algorithms.
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:2310. 15976v4 Announce Type: replace Abstract: signSGD is attractive in nonconvex optimization because it communicates sign-valued rather than full-precision gradients.
arXiv:2602. 20971v3 Announce Type: replace-cross Abstract: Bubeck and Selke (2021) propose the connection between the Law of Robustness and robust generalization error as an open problem.
arXiv:2606. 32005v1 Announce Type: cross Abstract: Stochastic Gradient Descent ($\textsf{SGD}$) is one of the most classical optimization algorithms with favorable theoretical guarantees, yet the practical implementation of $\textsf{SGD}$ differs subtly from its well-known form and is often referred to as Shuffling Stochastic Gradient Descent ($\textsf{Shuffling SGD}$).
arXiv:2606. 18463v1 Announce Type: cross Abstract: Distributed stochastic gradient descent (SGD) is limited by communication rather than computation, since each iteration requires an AllReduce across processes.
arXiv:2409. 19279v2 Announce Type: replace-cross Abstract: Continuous-time models can reveal accelerated structures in distributed optimization, but their rates need not survive direct discretization.
arXiv:2606. 24879v1 Announce Type: cross Abstract: We study the last iterate of the stochastic subgradient method for one-dimensional convex Lipschitz objectives.
arXiv:2607. 15412v1 Announce Type: new Abstract: Multi-objective learning (MOL) aims to optimize multiple objectives simultaneously.
arXiv:2604. 11151v2 Announce Type: replace Abstract: We develop parameter-free algorithms for unconstrained online learning with regret guarantees that scale with the gradient variation $V_T(u) = \sum_{t=2}^T \|\nabla f_t(u)-\nabla f_{t-1}(u)\|^2$.