On PI Controllers for Updating Lagrange Multipliers in Constrained Optimization
Fuente:
arXiv
Saved in:
| Main Authors: | , , , , |
|---|---|
| Format: | Preprint |
| Published: |
2024
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866911909926666240 |
|---|---|
| author | Sohrabi, Motahareh Ramirez, Juan Zhang, Tianyue H. Lacoste-Julien, Simon Gallego-Posada, Jose |
| author_facet | Sohrabi, Motahareh Ramirez, Juan Zhang, Tianyue H. Lacoste-Julien, Simon Gallego-Posada, Jose |
| contents | 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 $ν$PI 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 $ν$PI controller. Moreover, we prove that $ν$PI generalizes popular momentum methods for single-objective minimization. Our experiments demonstrate that $ν$PI reliably stabilizes the multiplier dynamics and its hyperparameters enjoy robust and predictable behavior. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2406_04558 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On PI Controllers for Updating Lagrange Multipliers in Constrained Optimization Sohrabi, Motahareh Ramirez, Juan Zhang, Tianyue H. Lacoste-Julien, Simon Gallego-Posada, Jose Machine Learning Optimization and Control 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 $ν$PI 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 $ν$PI controller. Moreover, we prove that $ν$PI generalizes popular momentum methods for single-objective minimization. Our experiments demonstrate that $ν$PI reliably stabilizes the multiplier dynamics and its hyperparameters enjoy robust and predictable behavior. |
| title | On PI Controllers for Updating Lagrange Multipliers in Constrained Optimization |
| topic | Machine Learning Optimization and Control |
| url | https://arxiv.org/abs/2406.04558 |