# End-to-End Feasible Optimization Proxies for Large-Scale Economic Dispatch

arXiv: https://arxiv.org/abs/2304.11726 · HTML: https://mlsanity.com/paper/2304.11726/

## Key facts

- Cited by 35 papers in the map (data through 14 Oct 2026).
- Builds on 33 of its 58 references that are in the map.
- First posted on arXiv 23 Apr 2023.

## Builds on (most cited first, 30 of 33)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Batch Normalization: Accelerating Deep Network Training by Reducing Internal Covariate Shift](https://mlsanity.com/paper/1502.03167/) (2015)
- [Differentiable Convex Optimization Layers](https://mlsanity.com/paper/1910.12430/) (2019)
- [DC3: A learning method for optimization with hard constraints](https://mlsanity.com/paper/2104.12225/) (2021)
- [Predicting AC Optimal Power Flows: Combining Deep Learning and Lagrangian Dual Methods](https://mlsanity.com/paper/1909.10461/) (2019)
- [Learning Optimal Solutions for Extremely Fast AC Optimal Power Flow](https://mlsanity.com/paper/1910.01213/) (2019)
- [The Power Grid Library for Benchmarking AC Optimal Power Flow Algorithms](https://mlsanity.com/paper/1908.02788/) (2019)
- [Optimal Power Flow Using Graph Neural Networks](https://mlsanity.com/paper/1910.09658/) (2019)
- [Self-Supervised Primal-Dual Learning for Constrained Optimization](https://mlsanity.com/paper/2208.09046/) (2022)
- [Physics-Informed Neural Networks for AC Optimal Power Flow](https://mlsanity.com/paper/2110.02672/) (2021)
- [DeepOPF: A Deep Neural Network Approach for Security-Constrained DC Optimal Power Flow](https://mlsanity.com/paper/1910.14448/) (2019)
- [JuMP: A Modeling Language for Mathematical Optimization](https://mlsanity.com/paper/1508.01982/) (2015)
- [DeepOPF: A Feasibility-Optimized Deep Neural Network Approach for AC Optimal Power Flow Problems](https://mlsanity.com/paper/2007.01002/) (2020)
- [Learning Optimization Proxies for Large-Scale Security-Constrained Economic Dispatch](https://mlsanity.com/paper/2112.13469/) (2021)
- [Topology-aware Graph Neural Networks for Learning Feasible and Adaptive ac-OPF Solutions](https://mlsanity.com/paper/2205.10129/) (2022)
- [Verification of Neural Network Behaviour: Formal Guarantees for Power System Applications](https://mlsanity.com/paper/1910.01624/) (2019)
- [Machine Learning for AC Optimal Power Flow](https://mlsanity.com/paper/1910.08842/) (2019)
- [Physics-Informed Neural Networks for Minimising Worst-Case Violations in DC Optimal Power Flow](https://mlsanity.com/paper/2107.00465/) (2021)
- [Learning to Solve Optimization Problems with Hard Linear Constraints](https://mlsanity.com/paper/2208.10611/) (2022)
- [Leveraging power grid topology in machine learning assisted optimal power flow](https://mlsanity.com/paper/2110.00306/) (2021)
- [AC Power Flow Data in MATPOWER and QCQP Format: iTesla, RTE Snapshots, and PEGASE](https://mlsanity.com/paper/1603.01533/) (2016)
- [Spatial Network Decomposition for Fast and Scalable AC-OPF Learning](https://mlsanity.com/paper/2101.06768/) (2021)
- [Unsupervised Optimal Power Flow Using Graph Neural Networks](https://mlsanity.com/paper/2210.09277/) (2022)
- [Statistical Learning For DC Optimal Power Flow](https://mlsanity.com/paper/1801.07809/) (2018)
- [Reduced Optimal Power Flow Using Graph Neural Network](https://mlsanity.com/paper/2206.13591/) (2022)
- [Compact Optimization Learning for AC Optimal Power Flow](https://mlsanity.com/paper/2301.08840/) (2023)
- [DNN-based Policies for Stochastic AC OPF](https://mlsanity.com/paper/2112.02441/) (2021)
- [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)
- [A Physics-Informed Machine Learning for Electricity Markets: A NYISO Case Study](https://mlsanity.com/paper/2304.00062/) (2023)
- [Optimal Power Flow Based on Physical-Model-Integrated Neural Network with Worth-Learning Data Generation](https://mlsanity.com/paper/2301.03766/) (2023)

## Built on by (most cited first, 30 of 35)

- [A Survey of Contextual Optimization Methods for Decision Making under Uncertainty](https://mlsanity.com/paper/2306.10374/) (2023)
- [HardNet: Hard-Constrained Neural Networks with Universal Approximation Guarantees](https://mlsanity.com/paper/2410.10807/) (2024)
- [Dual Conic Proxies for AC Optimal Power Flow](https://mlsanity.com/paper/2310.02969/) (2023)
- [Dual Lagrangian Learning for Conic Optimization](https://mlsanity.com/paper/2402.03086/) (2024)
- [PGLearn -- An Open-Source Learning Toolkit for Optimal Power Flow](https://mlsanity.com/paper/2505.22825/) (2025)
- [Enforcing Hard Linear Constraints in Deep Learning Models with Decision Rules](https://mlsanity.com/paper/2505.13858/) (2025)
- [Learning to Optimize for Mixed-Integer Non-linear Programming with Feasibility Guarantees](https://mlsanity.com/paper/2410.11061/) (2024)
- [AI4OPT: AI Institute for Advances in Optimization](https://mlsanity.com/paper/2307.02671/) (2023)
- [Dual Interior Point Optimization Learning](https://mlsanity.com/paper/2402.02596/) (2024)
- [Towards graph neural networks for provably solving convex optimization problems](https://mlsanity.com/paper/2502.02446/) (2025)
- [PROPEL: Supervised and Reinforcement Learning for Large-Scale Supply Chain Planning](https://mlsanity.com/paper/2504.07383/) (2025)
- [Optimization-based Learning for Dynamic Load Planning in Trucking Service Networks](https://mlsanity.com/paper/2307.04050/) (2023)
- [Self-Supervised Learning for Large-Scale Preventive Security Constrained DC Optimal Power Flow](https://mlsanity.com/paper/2311.18072/) (2023)
- [Compact Optimality Verification for Optimization Proxies](https://mlsanity.com/paper/2405.21023/) (2024)
- [Tightening optimality gap with confidence through conformal prediction](https://mlsanity.com/paper/2503.04071/) (2025)
- [Sobolev Training of End-to-End Optimization Proxies](https://mlsanity.com/paper/2505.11342/) (2025)
- [Smart Surrogate Losses for Contextual Stochastic Linear Optimization with Robust Constraints](https://mlsanity.com/paper/2505.22881/) (2025)
- [RL-SPH: Learning to Achieve Feasible Solutions for Integer Linear Programs](https://mlsanity.com/paper/2411.19517/) (2024)
- [Dual Conic Proxy for Semidefinite Relaxation of AC Optimal Power Flow](https://mlsanity.com/paper/2502.06978/) (2025)
- [Differentiable Optimization for Deep Learning-Enhanced DC Approximation of AC Optimal Power Flow](https://mlsanity.com/paper/2504.01970/) (2025)
- [Partially-Supervised Neural Network Model For Quadratic Multiparametric Programming](https://mlsanity.com/paper/2506.05567/) (2025)
- [ID-PaS+ : Identity-Aware Predict-and-Search for General Mixed-Integer Linear Programs](https://mlsanity.com/paper/2512.10211/) (2025)
- [Operational risk quantification of power grids using graph neural network surrogates of the DC OPF](https://mlsanity.com/paper/2311.03661/) (2023)
- [Toward Rapid, Optimal, and Feasible Power Dispatch through Generalized Neural Mapping](https://mlsanity.com/paper/2311.04838/) (2023)
- [Impact of Data Poisoning Attacks on Feasibility and Optimality of Neural Power System Optimizers](https://mlsanity.com/paper/2502.05727/) (2025)
- [Navigating Demand Uncertainty in Container Shipping: Deep Reinforcement Learning for Enabling Adaptive and Feasible Master Stowage Planning](https://mlsanity.com/paper/2502.12756/) (2025)
- [Learning-Augmented Power System Operations: A Unified Optimization View](https://mlsanity.com/paper/2505.05203/) (2025)
- [Learning to Solve Constrained Bilevel Control Co-Design Problems](https://mlsanity.com/paper/2507.09050/) (2025)
- [OptiProxy-NAS: Optimization Proxy based End-to-End Neural Architecture Search](https://mlsanity.com/paper/2509.05656/) (2025)
- [Self-Certifying Primal-Dual Optimization Proxies for Large-Scale Batch Economic Dispatch](https://mlsanity.com/paper/2510.15850/) (2025)

## Abstract (arXiv)

The paper proposes a novel End-to-End Learning and Repair (E2ELR) architecture for training optimization proxies for economic dispatch problems. E2ELR combines deep neural networks with closed-form, differentiable repair layers, thereby integrating learning and feasibility in an end-to-end fashion. E2ELR is also trained with self-supervised learning, removing the need for labeled data and the solving of numerous optimization problems offline. E2ELR is evaluated on industry-size power grids with tens of thousands of buses using an economic dispatch that co-optimizes energy and reserves. The results demonstrate that the self-supervised E2ELR achieves state-of-the-art performance, with optimality gaps that outperform other baselines by at least an order of magnitude.