Anytime Acceleration of Gradient Descent

2024/11/26 by Zihan Zhang, Zhang, Zihan, Jason D. Lee +5 · 3 voices · 2 citations
Engineering · #Welding Techniques and Residual Stresses #cs.LG #eess.SY #math.OC #stat.ML

paper · pdf · doi:10.48550/arxiv.2411.17668

openalex publication_date 2024/11/26 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/30

Abstract

This work investigates stepsize-based acceleration of gradient descent with \em anytime convergence guarantees. For smooth (non-strongly) convex optimization, we propose a stepsize schedule that allows gradient descent to achieve convergence guarantees of O(T^-1.119) for any stopping time T, where the stepsize schedule is predetermined without prior knowledge of the stopping time. This result provides an affirmative answer to a COLT open problem \citepkornowski2024open regarding whether stepsize-based acceleration can yield anytime convergence rates of o(T^-1). We further extend our theory to yield anytime convergence guarantees of exp(-Ω(T/κ^0.893)) for smooth and strongly convex optimization, with κ being the condition number.

Cited by

• Generalization of Silver Stepsize Schedule to Stochastic Optimization
• Adaptive control mechanisms in gradient descent algorithms

Discussions

• arxiv.org/abs/2411.17668 Our postdoc zihan slays another COLT open problem! proceedings.mlr.press/v247/kornows... [bsky, 67 points, 1 comments]
• Gradient Descent with large stepsizes converges faster than O(1/T) but it was only shown for the *best* iterate before. Cool to see new results showing we can also get an improvement for the last iter [bsky, 10 points, 1 comments]
• Very cool stuff: arxiv.org/abs/2411.17668 [bsky, 0 points, 0 comments]

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