arXiv：cs.LG· Utkarsh Grover, Wyatt Mackey, Kaixun Hua, J. Morris Chang, Xiaomin Lin·· 4 小时前AI 评分31
ORACLE：面向约束学习的优化器相对对齐方法
ORACLE: Optimizer-Relative Alignment for Constrained LEarning
AI 导读
研究者提出 ORACLE，一种在优化器更新后评估约束兼容性的约束学习方法，通过异构约束族的联合端点线性化构造对齐、限制其权限并在验证后提交。在八个偏微分方程基准和四种优化器（涵盖欧氏、对角自适应与结构化预条件几何）上，ORACLE 在 94% 配置中优于或持平原生优化器，跨模型分析中同一比例为 92%。
正文
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.
| Subjects: | Machine Learning (cs.LG) |
| Cite as: | arXiv:2610.09040 [cs.LG] |
| (or arXiv:2610.09040v1 [cs.LG] for this version) | |
| https://doi.org/10.48550/arXiv.2610.09040 arXiv-issued DOI via DataCite (pending registration) |
Submission history
From: Utkarsh Grover [view email]
[v1]
Tue, 6 Oct 2026 19:41:51 UTC (1,563 KB)
来源：arXiv：cs.LG · arxiv.org