发表机构
ETH Zürich（苏黎世联邦理工学院）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文提出投影自适应损失（PAL），通过单个分离投影步骤实现精确约束满足，训练速度比现有方法快2.5倍，并在非线性约束下保持近乎完美可行性。
AI 中文摘要
精确的约束满足是在许多领域部署学习模型的前提，这促使了通过修复程序来修正原始神经预测的方法。当前方法在训练中展开多个修复步骤，并对展开后仍存在的约束违反进行软惩罚。这既计算密集又内存密集，在修复未能收敛时缺乏鲁棒性，并且将大部分约束满足工作交给了修复过程。我们的核心发现是，与常见做法相反，在训练中单个分离的投影步骤就足够了。我们通过投影自适应损失（PAL）实现了这一点，该损失利用此单步后的约束残差来自适应地加权原始预测上的约束惩罚。在实验中，PAL 是唯一在极度非线性约束上保持几乎完美可行性的方法，并在合成和工程基准上匹配或优于当前方法。由于它仅需要单个分离的投影步骤，PAL 在其自身的 ACOPF 基准上训练速度比典型的基于修复的方法（DC3）快 2.5 倍。PAL 还可以在约束评估昂贵（例如，通过神经代理）的情况下进行训练，而当前展开方法在这种设置下内存不可行。
英文摘要
Precise constraint satisfaction is a prerequisite to deploying learned models in many areas, motivating methods that repair raw neural predictions with a repair procedure. Current methods unroll multiple repair steps in training and softly penalize constraint violations that remain after the unroll. This is compute- and memory-intensive, lacks robustness when the repair fails to converge, and surrenders most of the constraint satisfaction work to the repair. Our central finding is that, contrary to common practice, a single detached projection step suffices in training. We accomplish this with a Projection-Adaptive Loss (PAL), which uses the constraint residual after this single step to adaptively weigh constraint penalties on the raw prediction. In experiments, PAL is the only method that retains virtually perfect feasibility on extremely nonlinear constraints, and matches or outperforms current methods on synthetic and engineering benchmarks. Because it only requires a single detached projection step, PAL trains 2.5x faster than the canonical repair-based method (DC3) on its own ACOPF benchmark. PAL can also be trained when constraints are expensive to evaluate (e.g., via neural surrogates), a setting where current unrolled methods are memory-intractable.
Comments36 pages, 11 figures, 12 tables. Code: https://github.com/IDEALLab/projection-adaptive-loss
