We study stochastic gradient descent (SGD) with gradient clipping on convex functions under a generalized smoothness assumption called (L0,L1)-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.
@article{arxiv.2502.16492,
title = {Convergence of Clipped SGD on Convex $(L_0,L_1)$-Smooth Functions},
author = {Ofir Gaash and Kfir Yehuda Levy and Yair Carmon},
journal= {arXiv preprint arXiv:2502.16492},
year = {2025}
}