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Adaptive SGD with Line-Search and Polyak Stepsizes: Nonconvex Convergence and Accelerated Rates

Published: November 25, 2025 | arXiv ID: 2511.20207v2

By: Haotian Wu

Potential Business Impact:

Helps computers solve hard math problems faster.

Business Areas:
A/B Testing Data and Analytics

We extend the convergence analysis of AdaSLS and AdaSPS in [Jiang and Stich, 2024] to the nonconvex setting, presenting a unified convergence analysis of stochastic gradient descent with adaptive Armijo line-search (AdaSLS) and Polyak stepsize (AdaSPS) for nonconvex optimization. Our contributions include: (1) an $\mathcal{O}(1/\sqrt{T})$ convergence rate for general nonconvex smooth functions, (2) an $\mathcal{O}(1/T)$ rate under quasar-convexity and interpolation, and (3) an $\mathcal{O}(1/T)$ rate under the strong growth condition for general nonconvex functions.

Page Count
15 pages

Category
Mathematics:
Optimization and Control