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arXiv · 2304.09221

Convergence of stochastic gradient descent under a local Lojasiewicz condition for deep neural networks

Jing An·Jianfeng Lu
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Abstract

We study the convergence of stochastic gradient descent (SGD) for non-convex objective functions. We establish the local convergence with positive probability under the local \L{}ojasiewicz condition introduced by Chatterjee in \cite{chatterjee2022convergence} and an additional local structural assumption of the loss function landscape. A key component of our proof is to ensure that the whole trajectories of SGD stay inside the local region with a positive probability. We also provide examples of neural networks with finite widths such that our assumptions hold.

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Jing An, Jianfeng Lu. 2023-04-18. Convergence of stochastic gradient descent under a local Lojasiewicz condition for deep neural networks. https://arxiv.org/abs/2304.09221

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