Abstract
Constraint handling methods typically intervene before the optimizer acts, by modifying the objective or the gradient. Yet momentum, adaptive scaling, and structured preconditioning can substantially reshape that signal before it becomes a parameter update. We formulate optimizer relative constrained learning, where constraint compatibility is assessed on the post optimizer update. Building on this view, we introduce ORACLE, which evaluates the native optimizer's realized step through a joint endpoint linearization of heterogeneous constraint families, constructs the resulting alignment in the optimizer's own geometry, bounds its authority, and commits it only after validation. We evaluate ORACLE across eight Partial Differential Equation benchmarks and four optimizers spanning Euclidean, diagonal adaptive, and structured preconditioned geometries, where it improves or matches native optimizer in 94% of configurations. Cross model analysis shows the same behavior in 92% of configurations, while matched comparisons show improvements over alternative constraint-handling methods acting at the objective, gradient, and post-optimizer levels.
Keywords
Publication details
- Journal
- Not available
- Open access
- Green open access
Cite this article
APA 7
Grover, U., Mackey, W., Hua, K., Chang, J. M., & Lin, X. (2026). ORACLE: Optimizer-Relative Alignment for Constrained LEarning. https://omanscience.com/en/articles/oracle-optimizer-relative-alignment-for-constrained-learning
MLA 9
Grover, Utkarsh, et al. "ORACLE: Optimizer-Relative Alignment for Constrained LEarning." https://omanscience.com/en/articles/oracle-optimizer-relative-alignment-for-constrained-learning.
Chicago (author–date)
Grover, Utkarsh, Wyatt Mackey, Kaixun Hua, J. Morris Chang, and Xiaomin Lin. 2026. "ORACLE: Optimizer-Relative Alignment for Constrained LEarning." https://omanscience.com/en/articles/oracle-optimizer-relative-alignment-for-constrained-learning.
Harvard
Grover, U., Mackey, W., Hua, K., Chang, J. M. and Lin, X. (2026) 'ORACLE: Optimizer-Relative Alignment for Constrained LEarning', Available at: https://omanscience.com/en/articles/oracle-optimizer-relative-alignment-for-constrained-learning.
Vancouver
Grover U, Mackey W, Hua K, Chang JM, Lin X. ORACLE: Optimizer-Relative Alignment for Constrained LEarning. https://omanscience.com/en/articles/oracle-optimizer-relative-alignment-for-constrained-learning
IEEE
U. Grover, W. Mackey, K. Hua, J. M. Chang, and X. Lin, "ORACLE: Optimizer-Relative Alignment for Constrained LEarning," https://omanscience.com/en/articles/oracle-optimizer-relative-alignment-for-constrained-learning.