连续时间随机梯度下降的收敛性及其在线性深度神经网络中的应用

arXiv - STAT - Machine Learning Pub Date : 2024-09-11 DOI:arxiv-2409.07401

Gabor Lugosi, Eulalia Nualart

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引用次数: 0

摘要

我们研究了随机梯度下降过程的连续时间近似值，用于最小化学习问题中的预期损失。主要结果建立了收敛的一般充分条件，扩展了 Chatterjee (2022) 为（非随机）梯度下降建立的结果。

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

We study a continuous-time approximation of the stochastic gradient descent process for minimizing the 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 linear neural network training.

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arXiv - STAT - Machine Learning

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