Generalized Gradient Norm Clipping & Non-Euclidean $(L_0,L_1)$-Smoothness

• URL: http://arxiv.org/abs/2506.01913v1
• Date: Mon, 02 Jun 2025 17:34:29 GMT
• Title: Generalized Gradient Norm Clipping & Non-Euclidean $(L_0,L_1)$-Smoothness
• Authors: Thomas Pethick, Wanyun Xie, Mete Erdogan, Kimon Antonakopoulos, Tony Silveti-Falls, Volkan Cevher,
• Abstract summary: This work introduces a hybrid non-Euclidean optimization method which generalizes norm clipping by combining steepest descent and conditional gradient approaches.<n>We discuss how to instantiate the algorithms for deep learning and demonstrate their properties on image classification and language modeling.
• Score: 51.302674884611335
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: 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 by leveraging a momentum based gradient estimator. We discuss how to instantiate the algorithms for deep learning and demonstrate their properties on image classification and language modeling.

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