@Article{JML-2-138,
author = {Ko , Taehee and Li , Xiantao},
title = {A Local Convergence Theory for the Stochastic Gradient Descent Method in Non-Convex Optimization with Non-Isolated Local Minima},
journal = {Journal of Machine Learning},
year = {2023},
volume = {2},
number = {2},
pages = {138--160},
abstract = {<p style="text-align: justify;">Loss functions with non-isolated minima have emerged in several machine-learning problems, creating a gap between theoretical predictions and observations in practice. In this paper, we formulate a new
type of local convexity condition that is suitable to describe the behavior of loss functions near non-isolated
minima. We show that such a condition is general enough to encompass many existing conditions. In addition,
we study the local convergence of the stochastic gradient descent (SGD) method under this mild condition by
adopting the notion of stochastic stability. In the convergence analysis, we establish concentration inequalities
for the iterates in SGD, which can be used to interpret the empirical observation from some practical training
results.</p>},
issn = {2790-2048},
doi = {https://doi.org/10.4208/jml.230106},
url = {http://global-sci.org/intro/article_detail/jml/21759.html}
}