发表机构
University of South Florida; DEVCOM Army Research Lab（南佛罗里达大学; DEVCOM陆军研究实验室）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
ORACLE提出在优化器更新后评估约束兼容性，通过联合端点线性化构建对齐，在多个PDE基准和优化器上显著优于或匹配原生方法。
AI 中文摘要
约束处理方法通常在优化器执行之前进行干预，通过修改目标函数或梯度来实现。然而，动量、自适应缩放和结构化预处理可以在信号成为参数更新之前大幅重塑该信号。我们提出了优化器相对约束学习，其中约束兼容性在优化器更新之后进行评估。基于这一观点，我们引入了ORACLE，它通过异构约束族的联合端点线性化来评估原生优化器实际执行的步骤，在优化器自身的几何结构中构建由此产生的对齐，限制其权限，并在验证后才提交。我们在八个偏微分方程基准测试和四个跨越欧几里得、对角自适应和结构化预处理几何结构的优化器上评估了ORACLE，其中在94%的配置中它优于或匹配原生优化器。跨模型分析显示在92%的配置中表现出相同行为，而匹配比较显示在目标、梯度和优化器后级别上优于替代约束处理方法。
英文摘要
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.
