Can we accelerate the convergence of gradient descent without changing the algorithm—
just by judiciously choosing stepsizes? Surprisingly, we show that the answer is yes. Our …

This work establishes new convergence guarantees for gradient descent in smooth convex
optimization via a computer-assisted analysis technique. Our theory allows nonconstant …

We provide a concise, self-contained proof that the Silver Stepsize Schedule proposed in
our companion paper directly applies to smooth (non-strongly) convex optimization …

This work considers gradient descent for L-smooth convex optimization with stepsizes larger
than the classic regime where descent can be ensured. The stepsize schedules considered …

Recently Grimmer [1] showed for smooth convex optimization by utilizing longer steps
periodically, gradient descent's state-of-the-art O (1/T) convergence guarantees can be …

Large learning rates, when applied to gradient descent for nonconvex optimization, yield
various implicit biases including the edge of stability (Cohen et al., 2021), balancing (Wang …

This work considers stepsize schedules for gradient descent on smooth convex objectives.
We extend the existing literature and propose a unified technique for constructing stepsizes …

In this paper, we focus on the relaxed proximal point algorithm (RPPA) for solving convex
(possibly nonsmooth) optimization problems. We conduct a comprehensive study on three …

This work investigates stepsize-based acceleration of gradient descent with {\em anytime}
convergence guarantees. For smooth (non-strongly) convex optimization, we propose a …

A prevalent belief among optimization specialists is that linear convergence of gradient
descent is contingent on the function growing quadratically away from its minimizers. In this …