# Self-Certifying Primal-Dual Optimization Proxies for Large-Scale Batch Economic Dispatch

arXiv: https://arxiv.org/abs/2510.15850 · HTML: https://mlsanity.com/paper/2510.15850/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 27 of its 36 references that are in the map.
- First posted on arXiv 17 Oct 2025.

## Builds on (most cited first, 27 of 27)

- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [OptNet: Differentiable Optimization as a Layer in Neural Networks](https://mlsanity.com/paper/1703.00443/) (2017)
- [Beta-CROWN: Efficient Bound Propagation with Per-neuron Split Constraints for Complete and Incomplete Neural Network Robustness Verification](https://mlsanity.com/paper/2103.06624/) (2021)
- [Algorithms for Verifying Deep Neural Networks](https://mlsanity.com/paper/1903.06758/) (2019)
- [Parallelizing the dual revised simplex method](https://mlsanity.com/paper/1503.01889/) (2015)
- [The Power Grid Library for Benchmarking AC Optimal Power Flow Algorithms](https://mlsanity.com/paper/1908.02788/) (2019)
- [Self-Supervised Primal-Dual Learning for Constrained Optimization](https://mlsanity.com/paper/2208.09046/) (2022)
- [JuMP 1.0: Recent improvements to a modeling language for mathematical optimization](https://mlsanity.com/paper/2206.03866/) (2022)
- [End-to-End Feasible Optimization Proxies for Large-Scale Economic Dispatch](https://mlsanity.com/paper/2304.11726/) (2023)
- [HardNet: Hard-Constrained Neural Networks with Universal Approximation Guarantees](https://mlsanity.com/paper/2410.10807/) (2024)
- [RAYEN: Imposition of Hard Convex Constraints on Neural Networks](https://mlsanity.com/paper/2307.08336/) (2023)
- [Physics-Informed Neural Networks for Minimising Worst-Case Violations in DC Optimal Power Flow](https://mlsanity.com/paper/2107.00465/) (2021)
- [Smart-PGSim: Using Neural Network to Accelerate AC-OPF Power Grid Simulation](https://mlsanity.com/paper/2008.11827/) (2020)
- [Pinet: Optimizing hard-constrained neural networks with orthogonal projection layers](https://mlsanity.com/paper/2508.10480/) (2025)
- [PDHG-Unrolled Learning-to-Optimize Method for Large-Scale Linear Programming](https://mlsanity.com/paper/2406.01908/) (2024)
- [Physics-Informed Neural Networks with Hard Nonlinear Equality and Inequality Constraints](https://mlsanity.com/paper/2507.08124/) (2025)
- [Compact Optimization Learning for AC Optimal Power Flow](https://mlsanity.com/paper/2301.08840/) (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)
- [Real-Time Risk Analysis with Optimization Proxies](https://mlsanity.com/paper/2310.00709/) (2023)
- [Dual Interior Point Optimization Learning](https://mlsanity.com/paper/2402.02596/) (2024)
- [Just-In-Time Learning for Operational Risk Assessment in Power Grids](https://mlsanity.com/paper/2209.12762/) (2022)
- [Scalable Exact Verification of Optimization Proxies for Large-Scale Optimal Power Flow](https://mlsanity.com/paper/2405.06109/) (2024)
- [Compact Optimality Verification for Optimization Proxies](https://mlsanity.com/paper/2405.21023/) (2024)
- [Karush-Kuhn-Tucker Condition-Trained Neural Networks (KKT Nets)](https://mlsanity.com/paper/2410.15973/) (2024)
- [Benders Decomposition using Graph Modeling and Multi-Parametric Programming](https://mlsanity.com/paper/2508.01100/) (2025)

## Abstract (arXiv)

Recent research has shown that optimization proxies can be trained to high fidelity, achieving average optimality gaps under 1% for large-scale problems. However, worst-case analyses show that there exist in-distribution queries that result in orders of magnitude higher optimality gap, making it difficult to trust the predictions in practice. This paper aims at striking a balance between classical solvers and optimization proxies in order to enable trustworthy deployments with interpretable speed-optimality tradeoffs based on a user-defined optimality threshold. To this end, the paper proposes a hybrid solver that leverages duality theory to efficiently bound the optimality gap of predictions, falling back to a classical solver for queries where optimality cannot be certified. To improve the achieved speedup of the hybrid solver, the paper proposes an alternative training procedure that combines the primal and dual proxy training. Experiments on large-scale transmission systems show that the hybrid solver is highly scalable. The proposed hybrid solver achieves speedups of over 1000x compared to a parallelized simplex-based solver while guaranteeing a maximum optimality gap of 2%.