# Learning for Constrained Optimization: Identifying Optimal Active Constraint Sets

arXiv: https://arxiv.org/abs/1802.09639 · HTML: https://mlsanity.com/paper/1802.09639/

## Key facts

- Cited by 36 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 26 Feb 2018.

## Built on by (most cited first, 30 of 36)

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- [Learning Regionally Decentralized AC Optimal Power Flows with ADMM](https://mlsanity.com/paper/2205.03787/) (2022)
- [Ensuring DNN Solution Feasibility for Optimization Problems with Convex Constraints and Its Application to DC Optimal Power Flow Problems](https://mlsanity.com/paper/2112.08091/) (2021)
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- [Graph Neural Networks for Learning Real-Time Prices in Electricity Market](https://mlsanity.com/paper/2106.10529/) (2021)
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- [HoP: Homeomorphic Polar Learning for Hard Constrained Optimization](https://mlsanity.com/paper/2502.00304/) (2025)
- [Partially-Supervised Neural Network Model For Quadratic Multiparametric Programming](https://mlsanity.com/paper/2506.05567/) (2025)
- [LEAF: A Learning-Enabled ADMM Framework for Accelerated Convex Optimization](https://mlsanity.com/paper/2606.08993/) (2026)
- [Energy System Digitization in the Era of AI: A Three-Layered Approach towards Carbon Neutrality](https://mlsanity.com/paper/2211.04584/) (2022)
- [A Sequential Deep Learning Algorithm for Sampled Mixed-integer Optimisation Problems](https://mlsanity.com/paper/2301.10703/) (2023)
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- [Online Planning of Power Flows for Power Systems Against Bushfires Using Spatial Context](https://mlsanity.com/paper/2404.13391/) (2024)
- [Machine Learning for Fairness-Aware Load Shedding: A Real-Time Solution via Identifying Binding Constraints](https://mlsanity.com/paper/2407.18989/) (2024)

## Abstract (arXiv)

In many engineered systems, optimization is used for decision making at time-scales ranging from real-time operation to long-term planning. This process often involves solving similar optimization problems over and over again with slightly modified input parameters, often under tight latency requirements. We consider the problem of using the information available through this repeated solution process to directly learn a model of the optimal solution as a function of the input parameters, thus reducing the need to solve computationally expensive large-scale parametric programs in real time. Our proposed method is based on learning relevant sets of active constraints, from which the optimal solution can be obtained efficiently. Using active sets as features preserves information about the physics of the system, enables interpretable models, accounts for relevant safety constraints, and is easy to represent and encode. However, the total number of active sets is also very large, as it grows exponentially with system size. The key contribution of this paper is a streaming algorithm that learns the relevant active sets from training samples consisting of the input parameters and the corresponding optimal solution, without any assumptions on the problem structure. The algorithm comes with theoretical performance guarantees, and is known to converge fast for problem instances with a small number of relevant active sets. It can thus be used to establish the practicability of the learning method. Through extensive experiments on the Optimal Power Flow problem, we observe that often only a few active sets are relevant in practice, suggesting that the active sets is the appropriate level of abstraction for a learning algorithm to target.