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Sample-wise Constrained Learning via a Sequential Penalty Approach with Applications in Image Processing

arXiv 2601.16812 ↗First posted 23 Jan 2026cs.LG eess.IV math.OCcited by 0

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Abstract (arXiv)

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.

Key facts. No citing papers in the map yet (data through 14 Oct 2026). Builds on 22 of its 36 references that are in the map. First posted on arXiv 23 Jan 2026.

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References · 22

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10 more
  1. 2022Controlled Sparsity via Constrained Optimization or: How I Learned to Stop Tuning Penalties and Love Constraintscited by 25
  2. 2020Training neural networks under physical constraints using a stochastic augmented Lagrangian approachcited by 20
  3. 2021Constrained Optimization to Train Neural Networks on Critical and Under-Represented Classescited by 19
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  6. 2013Penalty Methods with Stochastic Approximation for Stochastic Nonlinear Programmingcited by 9
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