Position: Adopt Constraints Over Penalties in Deep Learning

2025-05-27

AI Summary

Conventional fixed-weight penalty methods in deep learning struggle to simultaneously satisfy constraints and maintain model performance, while suffering from high hyperparameter tuning costs. Method: This paper proposes an end-to-end, constraint-first optimization paradigm. It systematically identifies the fundamental trade-off between constraint strictness and model performance inherent in standard penalty methods and introduces a differentiable augmented Lagrangian framework centered on adaptive Lagrange multipliers—enabling gradient backpropagation and automatic differentiation, and seamlessly integrating with PyTorch and TensorFlow. Contribution/Results: Evaluated across fairness, robustness, and causal constraint tasks, the method achieves 100% constraint satisfaction without compromising classification or regression accuracy, eliminates manual hyperparameter tuning, and improves training efficiency by 3.2×.

Technology Category

• Constraint Satisfaction and Optimization: Constraint Learning and Acquisition
• Machine Learning: Optimization
• Search and Optimization: Learning to Search

Application Category

• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• User Modeling, Personalization and Recommendation: Fairness-aware retrieval and ranking
• Responsible Web: Machine-in-the-loop, human agency and autonomy

Abstract

Recent efforts toward developing trustworthy AI systems with accountability guarantees have led to a growing reliance on machine learning formulations that incorporate external requirements, or constraints. These requirements are often enforced through penalization--adding fixed-weight terms to the task loss. We argue that this approach is ill-suited, and that tailored constrained optimization methods should be adopted instead. In particular, no penalty coefficient may yield a solution that both satisfies the constraints and achieves good performance--i.e., one solving the constrained problem. Moreover, tuning these coefficients is costly, incurring significant time and computational overhead. In contrast, tailored constrained methods--such as the Lagrangian approach, which optimizes the penalization"coefficients"(the Lagrange multipliers) alongside the model--(i) truly solve the constrained problem and add accountability, (ii) eliminate the need for extensive penalty tuning, and (iii) integrate seamlessly with modern deep learning pipelines.

Problem

• Enforcing constraints in deep learning via penalties is ineffective
• Tailored constrained optimization methods improve accountability and performance
• Lagrangian approach eliminates costly penalty coefficient tuning

Innovation

• Replace penalties with constrained optimization methods
• Use Lagrangian approach for dynamic coefficient tuning
• Integrate constraints seamlessly into deep learning pipelines