README.md

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title: README
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# LearningToOptimize

## 1. Introduction

**LearningToOptimize** is an organization dedicated to **learning to optimize (L2O)** — an emerging paradigm where machine learning models *learn* to solve optimization problems efficiently. This approach is also known as using **optimization proxies** or **amortized optimization**. Our mission is to serve as a hub for sharing open datasets, pre-trained models, and tools that accelerate research and practical applications of L2O methods.

This organization is closely linked to the [LearningToOptimize.jl](https://github.com/andrewrosemberg/LearningToOptimize.jl) Julia package, which provides foundational functionalities for fitting ML-based surrogate models (or proxies) to complex optimization problems. Here, you will find:

- **Datasets**: Collections of problem instances and their optimal solutions, useful for training and benchmarking.  
- **Trained Models**: Ready-to-use optimization proxies for various tasks, enabling rapid inference on new problem instances.  
- **Benchmarking Tools**: Utilities for comparing learned proxies against traditional solvers in terms of speed, feasibility, and performance.

## 2. What are Optimization Proxies?

### High-Level Explanation

*Optimization proxies* are machine learning models that approximate or replace traditional optimization solvers. By observing many instances of a problem (and possibly their solutions), a proxy learns to predict near-optimal solutions in a single forward pass. This amortized approach can reduce or eliminate the need to run a time-consuming solver from scratch for each new instance, delivering **major speed-ups** in real-world applications such as power systems, resource allocation, and beyond.

### Technical Explanation

In more technical terms, **amortized optimization** seeks to learn a function \\( f_\theta(x) \\) that maps problem parameters \\( x \\) to solutions \\( y \\) that (approximately) minimize a given objective function subject to constraints. Modern methods leverage techniques like **differentiable optimization layers**, **input-convex neural networks**, or constraint-enforcing architectures (e.g., [DC3](https://openreview.net/pdf?id=0Ow8_1kM5Z)) to ensure that the learned proxy solutions are both feasible and performant. By coupling the solver and the model in an **end-to-end** pipeline, these approaches let the training objective directly reflect downstream metrics, improving speed and reliability.

Recent advances also focus on **trustworthy** or **certifiable** proxies, where constraint satisfaction or performance bounds are guaranteed. This is crucial in domains like energy systems or manufacturing, where infeasible solutions can have large penalties or safety concerns. Overall, learning-based optimization frameworks aim to combine the advantages of ML (data-driven generalization) with the rigor of mathematical programming (constraint handling and optimality).

For a broader overview, see the [SIAM News article on trustworthy optimization proxies](https://www.siam.org/publications/siam-news/articles/fusing-artificial-intelligence-and-optimization-with-trustworthy-optimization-proxies/), which highlights the growing synergy between AI and classical optimization.

## 3. References and Citations

1. **A. Rosemberg, M. Tanneau, B. Fanzeres, J. Garcia, P. Van Hentenryck (2023)**  
   *Learning Optimal Power Flow Value Functions with Input-Convex Neural Networks.*  
   Accepted at *PSCC 2024*.

3. **P. Donti, B. Amos, J. Z. Kolter (2021)**  
   *DC3: A Learning Method for Optimization with Hard Constraints.*  
   [ICLR](https://openreview.net/forum?id=0Ow8_1kM5Z)

4. **P. Van Hentenryck (2023)**  
   *Fusing Artificial Intelligence and Optimization with Trustworthy Optimization Proxies.*  
   [SIAM News](https://www.siam.org/publications/siam-news/articles/fusing-artificial-intelligence-and-optimization-with-trustworthy-optimization-proxies/)

5. **B. Amos (2022)**  
   *Tutorial on Amortized Optimization.*  
   [arXiv:2202.00665](https://arxiv.org/abs/2202.00665)

2. **A. Rosemberg, A. Street, D. M. Valladão, P. Van Hentenryck (2023)**  
   *Efficiently Training Deep-Learning Parametric Policies using Lagrangian Duality.*  
   [arXiv:2405.14973](https://arxiv.org/abs/2405.14973)

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By sharing our work and resources here, we hope to foster collaboration among researchers and practitioners who are exploring the exciting intersections of AI and optimization. Thank you for visiting **LearningToOptimize**—let’s push the boundaries of what’s possible in end-to-end optimization together!

Please reach out if you want to contribute!