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arXiv · 2502.16492

Convergence of Clipped SGD on Convex $(L_0,L_1)$-Smooth Functions

Ofir Gaash·Kfir Yehuda Levy·Yair Carmon
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Abstract

We study stochastic gradient descent (SGD) with gradient clipping on convex functions under a generalized smoothness assumption called $(L_0,L_1)$-smoothness. Using gradient clipping, we establish a high probability convergence rate that matches the SGD rate in the $L$ smooth case up to polylogarithmic factors and additive terms. We also propose a variation of adaptive SGD with gradient clipping, which achieves the same guarantee. We perform empirical experiments to examine our theory and algorithmic choices.

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Ofir Gaash, Kfir Yehuda Levy, Yair Carmon. 2025-02-23. Convergence of Clipped SGD on Convex $(L_0,L_1)$-Smooth Functions. https://arxiv.org/abs/2502.16492

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