Nesterov acceleration in benignly non-convex landscapes

• URL: http://arxiv.org/abs/2410.08395v1
• Date: Thu, 10 Oct 2024 22:02:10 GMT
• Title: Nesterov acceleration in benignly non-convex landscapes
• Authors: Kanan Gupta, Stephan Wojtowytsch,
• Abstract summary: We show that momentum-based optimization algorithms can be used in the notoriously non- convex setting of deep learning problems. In this article, we partially close this gap between the accelerated theory and practice setting.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: While momentum-based optimization algorithms are commonly used in the notoriously non-convex optimization problems of deep learning, their analysis has historically been restricted to the convex and strongly convex setting. In this article, we partially close this gap between theory and practice and demonstrate that virtually identical guarantees can be obtained in optimization problems with a `benign' non-convexity. We show that these weaker geometric assumptions are well justified in overparametrized deep learning, at least locally. Variations of this result are obtained for a continuous time model of Nesterov's accelerated gradient descent algorithm (NAG), the classical discrete time version of NAG, and versions of NAG with stochastic gradient estimates with purely additive noise and with noise that exhibits both additive and multiplicative scaling.

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