2024/06/07 by Motahareh Sohrabi, Juan M. Ramı́rez, Sohrabi, Motahareh +7 · 4 citations
Engineering · #Advanced Control Systems Design #Advanced Control Systems Optimization #FOS: Computer and information sciences #FOS: Mathematics #Machine Learning (cs.LG) #Optimization and Control (math.OC) #Stability and Control of Uncertain Systems
paper · pdf · doi:10.48550/arxiv.2406.04558
openalex publication_date 2024/06/07 · openalex created_date 2024/06/11 · openalex updated_date 2026/07/28
Constrained optimization offers a powerful framework to prescribe desired behaviors in neural network models. Typically, constrained problems are solved via their min-max Lagrangian formulations, which exhibit unstable oscillatory dynamics when optimized using gradient descent-ascent. The adoption of constrained optimization techniques in the machine learning community is currently limited by the lack of reliable, general-purpose update schemes for the Lagrange multipliers. This paper proposes the νPI algorithm and contributes an optimization perspective on Lagrange multiplier updates based on PI controllers, extending the work of Stooke, Achiam and Abbeel (2020). We provide theoretical and empirical insights explaining the inability of momentum methods to address the shortcomings of gradient descent-ascent, and contrast this with the empirical success of our proposed νPI controller. Moreover, we prove that νPI generalizes popular momentum methods for single-objective minimization. Our experiments demonstrate that νPI reliably stabilizes the multiplier dynamics and its hyperparameters enjoy robust and predictable behavior.