Tootfinder

Generalized Gradient Norm Clipping & Non-Euclidean $(L_0,L_1)$-Smoothness
Thomas Pethick, Wanyun Xie, Mete Erdogan, Kimon Antonakopoulos, Tony Silveti-Falls, Volkan Cevher
https://arxiv.org/abs/2506.01913

Generalized Gradient Norm Clipping & Non-Euclidean $(L_0,L_1)$-Smoothness
This work introduces a hybrid non-Euclidean optimization method which generalizes gradient norm clipping by combining steepest descent and conditional gradient approaches. The method achieves the best of both worlds by establishing a descent property under a generalized notion of ($L_0$,$L_1$)-smoothness. Weight decay is incorporated in a principled manner by identifying a connection to the Frank-Wolfe short step. In the stochastic case, we show an order optimal $O(n^{-1/4})$ convergence rate b…

This https://arxiv.org/abs/2502.16492 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

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

This https://arxiv.org/abs/2412.19529 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Nonconvex Stochastic Optimization under Heavy-Tailed Noises: Optimal Convergence without Gradient Clipping
Recently, the study of heavy-tailed noises in first-order nonconvex stochastic optimization has gotten a lot of attention since it was recognized as a more realistic condition as suggested by many empirical observations. Specifically, the stochastic noise (the difference between the stochastic and true gradient) is considered to have only a finite $\mathfrak{p}$-th moment where $\mathfrak{p}\in\left(1,2\right]$ instead of assuming it always satisfies the classical finite variance assumption. To…

This https://arxiv.org/abs/2412.19529 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Nonconvex Stochastic Optimization under Heavy-Tailed Noises: Optimal Convergence without Gradient Clipping
Recently, the study of heavy-tailed noises in first-order nonconvex stochastic optimization has gotten a lot of attention since it was recognized as a more realistic condition as suggested by many empirical observations. Specifically, the stochastic noise (the difference between the stochastic and true gradient) is considered to have only a finite $\mathfrak{p}$-th moment where $\mathfrak{p}\in\left(1,2\right]$ instead of assuming it always satisfies the classical finite variance assumption. To…