arXiv Machine Learning
Aug 12

A lower bound for stepsize-based acceleration of gradient descent

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.

By Jianhao Ma, Yuxin Chen
arXiv Machine Learning
5d ago

On the Last-Iterate Convergence of Clipped Gradient Methods

The paper establishes the first optimal last‑iterate convergence rates, in high probability, for Clipped‑SGD when the gradient noise is heavy‑tailed. It addresses the gap left by earlier results that required strong noise assumptions, such as exponentially decaying tails. By proving these rates, the authors provide theoretical support for the practical effectiveness of gradient clipping in stochastic convex optimization.

By Zijian Liu