The paper introduces ORACLE, a method for constrained learning that evaluates constraint compatibility after the optimizer has taken a step, rather than before. ORACLE performs a joint endpoint linearization of diverse constraint families, constructs an alignment in the optimizer’s geometry, bounds its authority, and commits the adjustment only after validation. Experiments on eight PDE benchmarks with four different optimizers show that ORACLE matches or improves performance in 94% of configurations, outperforming other constraint-handling approaches.
By Utkarsh Grover, Wyatt Mackey, Kaixun Hua, J. Morris Chang, Xiaomin Lin
The article "Constraint Learning by Optimizing over Trained Neural Networks: A Pragmatic Tutorial" discusses the emerging paradigm of embedding trained machine learning models, particularly neural networks, into optimization problems. It explains how constraints can be learned from data or objectives approximated to simplify models, while addressing challenges of size and speed. The tutorial offers practical guidance and demonstrates benefits through a case study that shows smaller, sparser networks can improve efficiency.
By Jiaxiao Fang, Thiago Serra
arXiv:2606. 13400v1 Announce Type: cross Abstract: While flow-based generative models have demonstrated strong performance across a wide range of domains, deploying them in safety-critical physical systems remains challenging due to strict constraint requirements.
By Jianming Ma, Qiyue Yang, Yang Zhang, Liyun Yan, Zhanxiang Cao, Yazhou Zhang, Yue Gao
Second-order cone programs (SOCPs) are a fundamental class of convex optimization problems widely applied across engineering domains. Classical interior-point methods are robust and accurate, but thei...
The paper presents a scalable learned iterative solver for nonlinear model predictive control (NMPC) that removes dependence on the prediction horizon by exploiting temporal decomposition in the network architecture. It introduces a closed‑loop resampling strategy to align training with deployment, achieving up to four‑fold speedups over IPOPT while maintaining comparable control performance and avoiding constraint violations. The method outperforms the previous monolithic LISCO approach on a CSTR cascade benchmark, scaling to larger problems without increasing network size.
By Lukas L\"uken, Sergio Lucia
arXiv:2605. 30456v2 Announce Type: replace Abstract: Many learning tasks in science and engineering are characterized by sparse datasets, which limits the effectiveness of purely data-driven approaches.
By Shraman Pal, Can Li
RAYEN is a framework that enforces hard convex constraints—linear, quadratic, second‑order cone, and linear matrix inequality—on neural network outputs or latent variables. It guarantees constraint satisfaction during both training and testing for any input and network weights without relying on expensive orthogonal projections, soft constraints, or iterative corrections. The method incurs negligible computational overhead, enabling rapid enforcement of thousands of constraints and significantly speeding up constrained trajectory optimization compared to existing algorithms.
By Jesus Tordesillas, Victor Klemm, Jonathan P. How, Marco Hutter
arXiv:2512.20270v2 Announce Type: replace-cross
Abstract: Many engineering tasks require solving families of nonlinear constrained optimization problems, parametrized in setting-specific variables. T...
By Matthias K. Hoffmann, Amine Othmane, Kathrin Fla{\ss}kamp
arXiv:2606. 09278v1 Announce Type: cross Abstract: Large Language Models frequently hallucinate in precision-critical domains such as technical diagramming and mechanical design, where outputs must satisfy strict geometric constraints.
By Rafael Cabral, Pang Zixi, Ziyi Shou, Shen Xin
arXiv:2610.08384v1 Announce Type: new
Abstract: In this work, we consider decision-focused learning (DFL) for a Markov decision process (MDP), where existing methods differentiate through the KKT con...
By Zihao Zhao, Ashwath K. Karunakaram, Ali Eshragh, Yuexing Li, Kai Wang
arXiv:2605.24437v2 Announce Type: replace
Abstract: We present a novel framework for embedding hard constraint satisfaction into neural network (NN) architectures, specifically feedforward neural net...
By Yang Zhao, Jungeun Lee, Jeong hwan Jeon, Sze Zheng Yong
In this work, we consider decision-focused learning (DFL) for a Markov decision process (MDP), where existing methods differentiate through the KKT conditions of the Bellman equation and require solvi...