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End-to-End Constrained Optimization Learning: A Survey

James Kotary, Ferdinando Fioretto, Pascal Van Hentenryck, Bryan Wilder

TL;DR

This paper surveys the emergence of end-to-end constrained optimization learning (E2E-COL), focusing on integrating machine learning with CO solvers and on data-driven prediction of CO solutions. It distinguishes two main directions: ML-augmented CO, where ML guides existing solvers, and End-to-End CO Learning, which embeds optimization within neural architectures to predict decisions directly. The survey analyzes Learning with Constraints, Learning Solutions on Graphs, and Predict-and-Optimize paradigms, highlighting differentiable optimization layers, RL and GNN-based methods, and their applicability to problems like LP/QP, MILP, TSP/VRP. It also outlines practical challenges—feasibility guarantees, runtime, benchmark standardization, and theoretical understanding—that must be addressed to realize widespread, reliable adoption in industry and research.

Abstract

This paper surveys the recent attempts at leveraging machine learning to solve constrained optimization problems. It focuses on surveying the work on integrating combinatorial solvers and optimization methods with machine learning architectures. These approaches hold the promise to develop new hybrid machine learning and optimization methods to predict fast, approximate, solutions to combinatorial problems and to enable structural logical inference. This paper presents a conceptual review of the recent advancements in this emerging area.

End-to-End Constrained Optimization Learning: A Survey

TL;DR

This paper surveys the emergence of end-to-end constrained optimization learning (E2E-COL), focusing on integrating machine learning with CO solvers and on data-driven prediction of CO solutions. It distinguishes two main directions: ML-augmented CO, where ML guides existing solvers, and End-to-End CO Learning, which embeds optimization within neural architectures to predict decisions directly. The survey analyzes Learning with Constraints, Learning Solutions on Graphs, and Predict-and-Optimize paradigms, highlighting differentiable optimization layers, RL and GNN-based methods, and their applicability to problems like LP/QP, MILP, TSP/VRP. It also outlines practical challenges—feasibility guarantees, runtime, benchmark standardization, and theoretical understanding—that must be addressed to realize widespread, reliable adoption in industry and research.

Abstract

This paper surveys the recent attempts at leveraging machine learning to solve constrained optimization problems. It focuses on surveying the work on integrating combinatorial solvers and optimization methods with machine learning architectures. These approaches hold the promise to develop new hybrid machine learning and optimization methods to predict fast, approximate, solutions to combinatorial problems and to enable structural logical inference. This paper presents a conceptual review of the recent advancements in this emerging area.

Paper Structure

This paper contains 18 sections, 17 equations, 2 figures.

Table of Contents

  1. Introduction
  2. Preliminaries: Constrained Optimization
  3. Optimization Solving Methods
  4. Preliminaries: Deep Learning
  5. Sequence Models
  6. Graph Neural Networks
  7. Overview of ML and CO
  8. ML-augmented CO
  9. E2E-COL: Predicting CO Solutions
  10. Learning with Constraints
  11. Learning Solutions on Graphs
  12. Supervised Learning
  13. Reinforcement Learning
  14. E2E-COL: Predict-and-Optimize
  15. Quadratic Programming
  16. ...and 3 more sections

Figures (2)

  • Figure 1: Machine Learning and Constrained Optimization.
  • Figure 2: Predict-and-optimize framework; gradients of a solver output (solution) must be computed with respect to its input (problem parameters) in order to maximize empirical model performance.