Motahareh Sohrabi

Collaborating Alumni - Université de Montréal

Supervisor

Simon Lacoste-Julien

Research Topics

Deep Learning

Optimization

Website

Publications

On PI Controllers for Updating Lagrange Multipliers in Constrained Optimization

Motahareh Sohrabi

Juan Ramirez

Tianyue H. Zhang

Simon Lacoste-Julien

Jose Gallego-Posada

Constrained optimization offers a powerful framework to prescribe desired behaviors in neural network models. Typically, constrained problem… (see more)s 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.

2024-07-08

Proceedings of the 41st International Conference on Machine Learning (published)

proceedings.mlr.press

openreview.net

Weight-Sharing Regularization

2024-04-18

Proceedings of The 27th International Conference on Artificial Intelligence and Statistics (published)

doi.org