Stochastic Gradient Descent Revisited

• URL: http://arxiv.org/abs/2412.06070v2
• Date: Sun, 09 Feb 2025 20:39:33 GMT
• Title: Stochastic Gradient Descent Revisited
• Authors: Azar Louzi,
• Abstract summary: gradient descent (SGD) has been a go-to algorithm for non gradient convergence problems in machine learning. This paper presents a full scope convergence theory and provides rates and complexities.
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• Abstract: Stochastic gradient descent (SGD) has been a go-to algorithm for nonconvex stochastic optimization problems arising in machine learning. Its theory however often requires a strong framework to guarantee convergence properties. We hereby present a full scope convergence study of biased nonconvex SGD, including weak convergence, function-value convergence and global convergence, and also provide subsequent convergence rates and complexities, all under relatively mild conditions in comparison with literature.

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