Mini-batch descent in semiflows

Document detail

ID

oai:arXiv.org:2407.07556

Topic

Mathematics - Optimization and Con... Mathematics - Numerical Analysis 34G25, 49J52, 37C10, 35K55, 37L05

Author

Corella, Alberto Domínguez Hernández, Martín

Year

2024

listing date

7/17/2024

Keywords

flow mini-batch descent gradient

Metrics

Abstract

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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