Theoretical Limits of Optimization: Gap in Accelerated Gradient Bounds Narrows to 0.66
prof_grimmer · x · 2026-08-12
This post provides background for the academic discussion on the acceleration limits of gradient descent stepsizes.
Previously, research by Jason Alterchuler, Pablo Parrilo, and others proved an acceleration effect of p=1.2716 was achievable. The new paper proves that the theoretical limit of p>1.9319 cannot be broken.
The author strongly believes the current p=1.2716 is tight even in asymptotic constants, meaning there is only a gap of 0.6603 left to resolve between the theoretical bounds.
Related event: GPT-Assisted Proof Reveals Theoretical Limits of Gradient Descent(4 posts)→
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