TY - JOUR
T1 - Convergence of Stochastic Gradient Descent under a Local Łojasiewicz Condition for Deep Neural Networks
AU - An , Jing
AU - Lu , Jianfeng
JO - Journal of Machine Learning
VL - 2
SP - 89
EP - 107
PY - 2025
DA - 2025/06
SN - 4
DO - http://doi.org/10.4208/jml.240724
UR - https://global-sci.org/intro/article_detail/jml/24143.html
KW - Non-convex optimization, Stochastic gradient descent, Convergence analysis.
AB - <p style="text-align: justify;">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 Łojasiewicz condition introduced
by Chatterjee [arXiv:2203.16462, 2022] 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.</p>