Mini-batch descent in semiflows

Hernández Salinas M, Dominguez Corella A (2025)

Publication Language: English

Publication Status: In review

Publication Type: Unpublished / Preprint

Future Publication Type: Journal article

Publication year: 2025

Open Access Link: https://arxiv.org/abs/2407.07556

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.

Authors with CRIS profile

Martin Hernández Salinas Lehrstuhl für Dynamics, Control, Machine Learning and Numerics (Alexander von Humboldt-Professur) Alberto Dominguez Corella Lehrstuhl für Dynamics, Control, Machine Learning and Numerics (Alexander von Humboldt-Professur)

How to cite

APA:

Hernández Salinas, M., & Dominguez Corella, A. (2025). Mini-batch descent in semiflows. (Unpublished, In review).

MLA:

Hernández Salinas, Martin, and Alberto Dominguez Corella. Mini-batch descent in semiflows. Unpublished, In review. 2025.

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