Silver Rate Is (Almost) Optimal for Gradient Descent Acceleration
Read the original on arXiv Machine Learning →The Flow has not summarised this story yet — read it at arXiv Machine Learning.
The Flow has not summarised this story yet — read it at arXiv Machine Learning.
arXiv:2609. 09152v2 Announce Type: replace-cross Abstract: We study how far gradient descent (GD) can be accelerated by predetermined stepsizes in smooth convex optimization.
The paper investigates the limits of accelerating gradient descent (GD) using predetermined step sizes in smooth convex optimization. It establishes new lower bounds: an ≥·n−1.6342 non‑anytime bound and an ≥·n−1.2408 anytime bound, surpassing previous results. These findings also demonstrate a strict separation between convergence exponents achievable in non‑anytime versus anytime settings.
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:2609.08537v1 Announce Type: cross Abstract: We study the time-uniform convergence of the raw iterate of standard stochastic gradient descent (SGD) for unconstrained smooth convex objectives. We...
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:2602. 12471v2 Announce Type: replace Abstract: We consider the optimization problem of minimizing the logistic loss with gradient descent to train a linear model for binary classification with separable data.