Position: Adopt Constraints Over Penalties in Deep Learning

Juan Ramirez, Meraj Hashemizadeh, Simon Lacoste-Julien

Abstract: Recent efforts to develop trustworthy AI systems with accountability guarantees have led to widespread use of machine learning formulations incorporating external requirements, or constraints. These requirements are often enforced via penalization--adding fixed-weight terms to the task loss. We argue this approach is fundamentally ill-suited since there may be no penalty coefficient that simultaneously ensures constraint satisfaction and optimal constrained performance, i.e., that truly solves the constrained problem. Moreover, tuning these coefficients requires costly trial-and-error, incurring significant time and computational overhead. We, therefore, advocate for broader adoption of tailored constrained optimization methods--such as the Lagrangian approach, which jointly optimizes the penalization "coefficients" (the Lagrange multipliers) and the model parameters. Such methods (i) truly solve the constrained problem and do so accountably, by clearly defining feasibility and verifying when it is achieved, (ii) eliminate the need for extensive penalty tuning, and (iii) integrate seamlessly with modern deep learning pipelines.