Sample-wise Constrained Learning via a Sequential Penalty Approach with Applications in Image Processing
Machine Learning
2026-01-26 v1 Image and Video Processing
Optimization and Control
Abstract
In many learning tasks, certain requirements on the processing of individual data samples should arguably be formalized as strict constraints in the underlying optimization problem, rather than by means of arbitrary penalties. We show that, in these scenarios, learning can be carried out exploiting a sequential penalty method that allows to properly deal with constraints. The proposed algorithm is shown to possess convergence guarantees under assumptions that are reasonable in deep learning scenarios. Moreover, the results of experiments on image processing tasks show that the method is indeed viable to be used in practice.
Cite
@article{arxiv.2601.16812,
title = {Sample-wise Constrained Learning via a Sequential Penalty Approach with Applications in Image Processing},
author = {Francesca Lanzillotta and Chiara Albisani and Davide Pucci and Daniele Baracchi and Alessandro Piva and Matteo Lapucci},
journal= {arXiv preprint arXiv:2601.16812},
year = {2026}
}