# Teaching Networks to Solve Optimization Problems

arXiv: https://arxiv.org/abs/2202.04104 · HTML: https://mlsanity.com/paper/2202.04104/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- Builds on 16 of its 43 references that are in the map.
- First posted on arXiv 8 Feb 2022.

## Builds on (most cited first, 16 of 16)

- [Deep Sets](https://mlsanity.com/paper/1703.06114/) (2017)
- [VoxelMorph: A Learning Framework for Deformable Medical Image Registration](https://mlsanity.com/paper/1809.05231/) (2018)
- [CVXPY: A Python-Embedded Modeling Language for Convex Optimization](https://mlsanity.com/paper/1603.00943/) (2016)
- [Learning to learn by gradient descent by gradient descent](https://mlsanity.com/paper/1606.04474/) (2016)
- [Gradient-based Hyperparameter Optimization through Reversible Learning](https://mlsanity.com/paper/1502.03492/) (2015)
- [Gradient Projection Memory for Continual Learning](https://mlsanity.com/paper/2103.09762/) (2021)
- [Fast Computation of Wasserstein Barycenters](https://mlsanity.com/paper/1310.4375/) (2013)
- [Generalized Sliced Wasserstein Distances](https://mlsanity.com/paper/1902.00434/) (2019)
- [Learning to Optimize: A Primer and A Benchmark](https://mlsanity.com/paper/2103.12828/) (2021)
- [Learning to Optimize](https://mlsanity.com/paper/1606.01885/) (2016)
- [OSQP: An Operator Splitting Solver for Quadratic Programs](https://mlsanity.com/paper/1711.08013/) (2017)
- [Learned Optimizers that Scale and Generalize](https://mlsanity.com/paper/1703.04813/) (2017)
- [Parameter Prediction for Unseen Deep Architectures](https://mlsanity.com/paper/2110.13100/) (2021)
- [DeepOPF: A Feasibility-Optimized Deep Neural Network Approach for AC Optimal Power Flow Problems](https://mlsanity.com/paper/2007.01002/) (2020)
- [Wasserstein Measure Coresets](https://mlsanity.com/paper/1805.07412/) (2018)
- [SLOSH: Set LOcality Sensitive Hashing via Sliced-Wasserstein Embeddings](https://mlsanity.com/paper/2112.05872/) (2021)

## Built on by (most cited first, 7 of 7)

- [Continuation Path Learning for Homotopy Optimization](https://mlsanity.com/paper/2307.12551/) (2023)
- [Optimization for Amortized Inverse Problems](https://mlsanity.com/paper/2210.13983/) (2022)
- [T-SKM-Net: Trainable Neural Network Framework for Linear Constraint Satisfaction via Sampling Kaczmarz-Motzkin Method](https://mlsanity.com/paper/2512.10461/) (2025)
- [Optimality-Informed Neural Networks for Solving Parametric Optimization Problems](https://mlsanity.com/paper/2512.20270/) (2025)
- [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)
- [SOVER: Formal Certification of Optimization Reformulations via LLM-Assisted SMT Verification](https://mlsanity.com/paper/2609.00728/) (2026)

## Abstract (arXiv)

Leveraging machine learning to facilitate the optimization process is an emerging field that holds the promise to bypass the fundamental computational bottleneck caused by classic iterative solvers in critical applications requiring near-real-time optimization. The majority of existing approaches focus on learning data-driven optimizers that lead to fewer iterations in solving an optimization. In this paper, we take a different approach and propose to replace the iterative solvers altogether with a trainable parametric set function, that outputs the optimal arguments/parameters of an optimization problem in a single feed forward. We denote our method as Learning to Optimize the Optimization Process (LOOP). We show the feasibility of learning such parametric (set) functions to solve various classic optimization problems including linear/nonlinear regression, principal component analysis, transport-based coreset, and quadratic programming in supply management applications. In addition, we propose two alternative approaches for learning such parametric functions, with and without a solver in the LOOP. Finally, through various numerical experiments, we show that the trained solvers could be orders of magnitude faster than the classic iterative solvers while providing near optimal solutions.