Stochastic Penalty-Barrier Methods for Constrained Machine Learning
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arXiv
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| Main Authors: | , , , , |
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| Format: | Preprint |
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2026
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| _version_ | 1866913146092912640 |
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| author | Bosák, Adam Kliachkin, Andrii Lepšová, Jana Bareilles, Gilles Mareček, Jakub |
| author_facet | Bosák, Adam Kliachkin, Andrii Lepšová, Jana Bareilles, Gilles Mareček, Jakub |
| contents | Constrained machine learning enables fairness-aware training, physics-informed neural networks, and integration of symbolic domain knowledge into statistical models. Despite its practical importance, no general method exists for the non-convex, non-smooth, stochastic setting that arises naturally in deep learning. We propose the Stochastic Penalty-Barrier Method (SPBM), which extends classical penalty and barrier methods to this setting via exponential dual averaging, a stabilized penalty schedule, and the Moreau envelope to handle non-smoothness. Experiments across multiple settings show that SPBM matches or outperforms existing constrained optimization baselines while incurring only linear runtime overhead compared to unconstrained Adam for up to 10,000 constraints. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_18618 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Stochastic Penalty-Barrier Methods for Constrained Machine Learning Bosák, Adam Kliachkin, Andrii Lepšová, Jana Bareilles, Gilles Mareček, Jakub Machine Learning Artificial Intelligence Constrained machine learning enables fairness-aware training, physics-informed neural networks, and integration of symbolic domain knowledge into statistical models. Despite its practical importance, no general method exists for the non-convex, non-smooth, stochastic setting that arises naturally in deep learning. We propose the Stochastic Penalty-Barrier Method (SPBM), which extends classical penalty and barrier methods to this setting via exponential dual averaging, a stabilized penalty schedule, and the Moreau envelope to handle non-smoothness. Experiments across multiple settings show that SPBM matches or outperforms existing constrained optimization baselines while incurring only linear runtime overhead compared to unconstrained Adam for up to 10,000 constraints. |
| title | Stochastic Penalty-Barrier Methods for Constrained Machine Learning |
| topic | Machine Learning Artificial Intelligence |
| url | https://arxiv.org/abs/2605.18618 |