Mini-batch descent in semiflows

Dominguez Corella A, Hernández Salinas M (2025)

Publication Language: English

Publication Type: Journal article

Publication year: 2025

Journal

Esaim-Control Optimisation and Calculus of Variations EDP Sciences

Book Volume: 31

Article Number: 28

DOI: 10.1051/cocv/2025018

Abstract

This paper investigates the application of mini-batch gradient descent to semiflows (gradient flows). Given a loss function (potential), 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 potential generating the semiflow, the mini-batch descent flow trajectory closely approximates the original semiflow trajectory on average. In addition, we study a randomized minimizing movement scheme that also approximates the semiflow of the full 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)

How to cite

APA:

Dominguez Corella, A., & Hernández Salinas, M. (2025). Mini-batch descent in semiflows. Esaim-Control Optimisation and Calculus of Variations, 31. https://doi.org/10.1051/cocv/2025018

MLA:

Dominguez Corella, Alberto, and Martin Hernández Salinas. "Mini-batch descent in semiflows." Esaim-Control Optimisation and Calculus of Variations 31 (2025).

BibTeX: Download