Document detail
ID
oai:arXiv.org:2407.07556
Topic
Mathematics - Optimization and Con... Mathematics - Numerical Analysis 34G25, 49J52, 37C10, 35K55, 37L05Author
Corella, Alberto Domínguez Hernández, MartínCategory
Computer Science
Year
2024
listing date
7/17/2024
Keywords
flow mini-batch descent gradientAbstract
This paper investigates the application of mini-batch gradient descent to semiflows.
Given a loss function, we introduce a continuous version of mini-batch gradient descent by randomly selecting sub-loss functions over time, defining a piecewise flow.
We prove that, under suitable assumptions on the gradient flow, the mini-batch descent flow trajectory closely approximates the original gradient flow trajectory on average.
Additionally, we propose a randomized minimizing movement scheme that also approximates the gradient flow of the loss function.
We illustrate the versatility of this approach across various problems, including constrained optimization, sparse inversion, and domain decomposition.
Finally, we validate our results with several numerical examples.
;Comment: 25 pages, 14 figures
Corella, Alberto Domínguez,Hernández, Martín, 2024, Mini-batch descent in semiflows
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