Position: Adopt Constraints Over Fixed Penalties in Deep Learning

2025/05/27 by Juan Ramírez, Ramirez, Juan, Meraj Hashemizadeh +3 · 2 citations
Computer Science · #Adversarial Robustness in Machine Learning #Explainable Artificial Intelligence (XAI) #FOS: Computer and information sciences #FOS: Mathematics #Machine Learning (cs.LG) #Optimization and Control (math.OC) #Stochastic Gradient Optimization Techniques

paper · pdf · doi:10.48550/arxiv.2505.20628

openalex publication_date 2025/05/27 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

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.

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Cited by

• Dual Optimistic Ascent (PI Control) is the Augmented Lagrangian Method in Disguise
• Benchmarking Stochastic Approximation Algorithms for Fairness-Constrained Training of Deep Neural Networks

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