Independently-Normalized SGD for Generalized-Smooth Nonconvex Optimization

• URL: http://arxiv.org/abs/2410.14054v1
• Date: Thu, 17 Oct 2024 21:52:00 GMT
• Title: Independently-Normalized SGD for Generalized-Smooth Nonconvex Optimization
• Authors: Yufeng Yang, Erin Tripp, Yifan Sun, Shaofeng Zou, Yi Zhou,
• Abstract summary: We show that many non machine learning problems meet that kind of condition that extends beyond traditional non-smoothepseps. We propose an independently-normalized gradient descent algorithm, which leverages independent sampling and normalization.
• Score: 19.000530691874516
• License:
• Abstract: Recent studies have shown that many nonconvex machine learning problems meet a so-called generalized-smooth condition that extends beyond traditional smooth nonconvex optimization. However, the existing algorithms designed for generalized-smooth nonconvex optimization encounter significant limitations in both their design and convergence analysis. In this work, we first study deterministic generalized-smooth nonconvex optimization and analyze the convergence of normalized gradient descent under the generalized Polyak-Lojasiewicz condition. Our results provide a comprehensive understanding of the interplay between gradient normalization and function geometry. Then, for stochastic generalized-smooth nonconvex optimization, we propose an independently-normalized stochastic gradient descent algorithm, which leverages independent sampling, gradient normalization and clipping to achieve an $\mathcal{O}(\epsilon^{-4})$ sample complexity under relaxed assumptions. Experiments demonstrate the fast convergence of our algorithm.

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