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

Haotian Wu

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arXiv · 2511.20207

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

Haotian Wu

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Abstract

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.

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Haotian Wu. 2025-11-25. Adaptive SGD with Line-Search and Polyak Stepsizes: Nonconvex Convergence and Accelerated Rates. https://arxiv.org/abs/2511.20207

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