Convergence of continuous-time stochastic gradient descent with applications to deep neural networks

Gabor Lugosi; Eulalia Nualart

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arXiv · 2409.07401

Convergence of continuous-time stochastic gradient descent with applications to deep neural networks

Gabor Lugosi·Eulalia Nualart

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Abstract

We study a continuous-time approximation of the stochastic gradient descent process for minimizing the population expected loss in learning problems. The main results establish general sufficient conditions for the convergence, extending the results of Chatterjee (2022) established for (nonstochastic) gradient descent. We show how the main result can be applied to the case of overparametrized neural network training.

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Gabor Lugosi, Eulalia Nualart. 2024-09-11. Convergence of continuous-time stochastic gradient descent with applications to deep neural networks. https://arxiv.org/abs/2409.07401

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