mlsanityData to 14 Oct 2026

Open Problem: Anytime Convergence Rate of Gradient Descent

arXiv 2406.13888 ↗First posted 19 Jun 2024math.OC cs.LGcited by 5

Not on the map. Why?

Abstract (arXiv)

Recent results show that vanilla gradient descent can be accelerated for smooth convex objectives, merely by changing the stepsize sequence. We show that this can lead to surprisingly large errors indefinitely, and therefore ask: Is there any stepsize schedule for gradient descent that accelerates the classic O(1/T) convergence rate, at any stopping time T?

Key facts. Cited by 5 papers in the map (data through 14 Oct 2026). Builds on 8 of its 11 references that are in the map. First posted on arXiv 19 Jun 2024.

Builds on

8 of 11 references.

References · 8

  1. 2014Convex Optimization: Algorithms and Complexitycited by 575
  2. 2021Acceleration Methodscited by 48
  3. 2023Provably Faster Gradient Descent via Long Stepscited by 20
  4. 2023Acceleration by Stepsize Hedging II: Silver Stepsize Schedule for Smooth Convex Optimizationcited by 20
  5. 2023Acceleration by Stepsize Hedging I: Multi-Step Descent and the Silver Stepsize Schedulecited by 19
  6. 2022Branch-and-Bound Performance Estimation Programming: A Unified Methodology for Constructing Optimal Optimization Methodscited by 16
  7. 2023Accelerated Gradient Descent via Long Stepscited by 9
  8. 2018First-order algorithms converge faster than O(1/k) on convex problemscited by 3

Built on by

Cited by year (2026 to 14 Oct)

Citing papers per year: 2024: 1; 2025: 0; 2026: 4.

5 papers.

  1. 2024Anytime Acceleration of Gradient Descentcited by 7
  2. 2026Gradient Descent's Last Iterate is Often (slightly) Suboptimalcited by 4
  3. 2026A lower bound for stepsize-based acceleration of gradient descentcited by 4
  4. 2026Improved Gradient Descent Lower Bounds Beyond Nesterovcited by 2
  5. 2026Silver Rate Is (Almost) Optimal for Gradient Descentcited by 1