# Learning to optimize: A tutorial for continuous and mixed-integer optimization

arXiv: https://arxiv.org/abs/2405.15251 · HTML: https://mlsanity.com/paper/2405.15251/

## Key facts

- Cited by 8 papers in the map (data through 14 Oct 2026).
- Builds on 11 of its 34 references that are in the map.
- First posted on arXiv 24 May 2024.

## Builds on (most cited first, 11 of 11)

- [Smart "Predict, then Optimize"](https://mlsanity.com/paper/1710.08005/) (2017)
- [On Hyperparameter Optimization of Machine Learning Algorithms: Theory and Practice](https://mlsanity.com/paper/2007.15745/) (2020)
- [From Predictive to Prescriptive Analytics](https://mlsanity.com/paper/1402.5481/) (2014)
- [ParamILS: An Automatic Algorithm Configuration Framework](https://mlsanity.com/paper/1401.3492/) (2014)
- [Learning to Select Cuts for Efficient Mixed-Integer Programming](https://mlsanity.com/paper/2105.13645/) (2021)
- [A Three-Operator Splitting Scheme and its Optimization Applications](https://mlsanity.com/paper/1504.01032/) (2015)
- [Efficient Neural Neighborhood Search for Pickup and Delivery Problems](https://mlsanity.com/paper/2204.11399/) (2022)
- [Adaptive Cut Selection in Mixed-Integer Linear Programming](https://mlsanity.com/paper/2202.10962/) (2022)
- [Machine Learning for Cutting Planes in Integer Programming: A Survey](https://mlsanity.com/paper/2302.09166/) (2023)
- [Benders Cut Classification via Support Vector Machines for Solving Two-stage Stochastic Programs](https://mlsanity.com/paper/1906.05994/) (2019)
- [Automatic MILP Solver Configuration By Learning Problem Similarities](https://mlsanity.com/paper/2307.00670/) (2023)

## Built on by (most cited first, 8 of 8)

- [Lightweight Deep Unfolding Networks with Enhanced Robustness for Infrared Small Target Detection](https://mlsanity.com/paper/2509.08205/) (2025)
- [An Efficient Unsupervised Framework for Convex Quadratic Programs via Deep Unrolling](https://mlsanity.com/paper/2412.01051/) (2024)
- [Accelerating Optimization via Differentiable Stopping Time](https://mlsanity.com/paper/2505.22509/) (2025)
- [Solving Max-Cut to Global Optimality via Feasibility-Preserving Graph Neural Networks](https://mlsanity.com/paper/2605.07113/) (2026)
- [Tuning-Free Structured Sparse PCA via Deep Unfolding Networks](https://mlsanity.com/paper/2502.20837/) (2025)
- [Neural Ising Machines via Unrolling and Zeroth-Order Training](https://mlsanity.com/paper/2602.00302/) (2026)
- [Deep Learning for Sequential Decision Making under Uncertainty: Foundations, Frameworks, and Frontiers](https://mlsanity.com/paper/2604.11507/) (2026)
- [DIFFRACT: Neuralized Utility Maximization for Wireless Networks by Differentiable Programming](https://mlsanity.com/paper/2606.07114/) (2026)

## Abstract (arXiv)

Learning to Optimize (L2O) stands at the intersection of traditional optimization and machine learning, utilizing the capabilities of machine learning to enhance conventional optimization techniques. As real-world optimization problems frequently share common structures, L2O provides a tool to exploit these structures for better or faster solutions. This tutorial dives deep into L2O techniques, introducing how to accelerate optimization algorithms, promptly estimate the solutions, or even reshape the optimization problem itself, making it more adaptive to real-world applications. By considering the prerequisites for successful applications of L2O and the structure of the optimization problems at hand, this tutorial provides a comprehensive guide for practitioners and researchers alike.