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arXiv · 2605.18618

Stochastic Penalty-Barrier Methods for Constrained Machine Learning

Adam Bosák·Andrii Kliachkin·Jana Lepšová·Gilles Bareilles·Jakub Mareček
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Abstract

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.

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Adam Bosák, Andrii Kliachkin, Jana Lepšová, Gilles Bareilles, Jakub Mareček. 2026-05-18. Stochastic Penalty-Barrier Methods for Constrained Machine Learning. https://arxiv.org/abs/2605.18618

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