mlsanityData to 14 Oct 2026

Gradient Methods with Online Scaling Part II. Practical Aspects

arXiv 2509.11007 ↗First posted 13 Sep 2025math.OC cs.LG stat.MLcited by 1

Not on the map. Why?

Abstract (arXiv)

Part I of this work [Gao25] establishes online scaled gradient methods (OSGM), a framework that utilizes online convex optimization to adapt stepsizes in gradient methods. This paper focuses on the practical aspects of OSGM. We leverage the OSGM framework to design new adaptive first-order methods and provide insights into their empirical behavior. The resulting method, OSGM-Best, matches the performance of quasi-Newton variants while requiring less memory and cheaper iterations. We also extend OSGM to nonconvex optimization and outline directions that connect OSGM to existing branches of optimization theory and practice.

Key facts. Cited by 1 paper in the map (data through 14 Oct 2026). Builds on 16 of its 42 references that are in the map. First posted on arXiv 13 Sep 2025.

Builds on

16 of 42 references.

References · 16

  1. 2014Adam: A Method for Stochastic Optimizationcited by 37,240
  2. 2019Introduction to Online Convex Optimizationcited by 803
  3. 2016Linear Convergence of Gradient and Proximal-Gradient Methods Under the Polyak-Lojasiewicz Conditioncited by 539
  4. 2019Online Learning: A Modern Introduction Using Convex Optimizationcited by 417
  5. 2017Online Learning Rate Adaptation with Hypergradient Descentcited by 118
  6. 2019Revisiting the Polyak step sizecited by 55
  7. 2021Acceleration Methodscited by 48
  8. 2021Stochastic Polyak Stepsize with a Moving Targetcited by 19
  9. 2018Lyapunov Functions for First-Order Methods: Tight Automated Convergence Guaranteescited by 11
  10. 2024Gradient Methods with Online Scalingcited by 11
  11. 2023Scalable Approximate Optimal Diagonal Preconditioningcited by 9
  12. 2018Non-monotone Behavior of the Heavy Ball Methodcited by 8
4 more
  1. 2023Automated tight Lyapunov analysis for first-order methodscited by 6
  2. 2025Provable and Practical Online Learning Rate Adaptation with Hypergradient Descentcited by 5
  3. 2025Gradient Methods with Online Scaling Part I. Theoretical Foundationscited by 3
  4. 2019Gradient methods exploiting spectral propertiescited by 1

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Cited by year (2026 to 14 Oct)

Citing papers per year: 2026: 1.

1 paper.

  1. 2026Optimizing the Preconditioner: A Black-box Online-to-Nonconvex Conversion with Static Regret Minimization Oraclescited by 0