mlsanityData to 14 Oct 2026

Position: Adopt Constraints Over Fixed Penalties in Deep Learning

arXiv 2505.20628 ↗First posted 27 May 2025cs.LG math.OCcited by 5

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Abstract (arXiv)

Recent efforts to develop trustworthy AI systems have increased interest in learning problems with explicit requirements, or constraints. In deep learning, however, such problems are often handled through fixed weighted-sum penalization: the constraints are added to the task loss with fixed coefficients, and the resulting scalarized objective is minimized. This position paper argues that fixed penalization is often ill-suited for deep learning problems with non-negotiable requirements for several reasons. First, in non-convex settings, the penalized and constrained problems are generally not equivalent, so solving the former need not solve the latter. Second, fixed penalization weakens hard requirements into soft penalties to be traded off against task performance. Third, choosing penalty coefficients to indirectly solve the constrained problem often involves costly trial and error, because changing them alters the penalized objective itself, and hence can mean solving the wrong problem altogether. We therefore argue that, when a deep learning problem specifies non-negotiable requirements, the constrained formulation itself should be the starting point, not the surrogate problem defined by fixed penalization. The appropriate solution strategy should then be chosen based on the problem's structure and scale.

Key facts. Cited by 5 papers in the map (data through 14 Oct 2026). Builds on 23 of its 48 references that are in the map. First posted on arXiv 27 May 2025.

Builds on

23 of 48 references.

References · 23

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11 more
  1. 2024HardNet: Hard-Constrained Neural Networks with Universal Approximation Guaranteescited by 31
  2. 2020Sequential Quadratic Optimization for Nonlinear Equality Constrained Stochastic Optimizationcited by 30
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Cited by year (2026 to 14 Oct)

Citing papers per year: 2025: 2; 2026: 3.

5 papers.

  1. 2025Dual Optimistic Ascent (PI Control) is the Augmented Lagrangian Method in Disguisecited by 1
  2. 2025Benchmarking Stochastic Approximation Algorithms for Fairness-Constrained Training of Deep Neural Networkscited by 0
  3. 2026CLASP: An online learning algorithm for Convex Losses And Squared Penaltiescited by 0
  4. 2026Global Optimality for Constrained Exploration via Penalty Regularizationcited by 0
  5. 2026Stochastic Penalty-Barrier Method for Constrained Machine Learningcited by 0