# Feasibility-Aware Imitation Learning for Benders Decomposition

arXiv: https://arxiv.org/abs/2604.04801 · HTML: https://mlsanity.com/paper/2604.04801/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Placed in Imitation learning methods, one of 13 directions in Offline RL and imitation learning from data.
- Builds on 15 of its 28 references that are in the map.
- First posted on arXiv 6 Apr 2026.

## Placed in

- Offline RL and imitation learning from data / [Imitation learning methods](https://mlsanity.com/offlinerl/imitation-learning-methods/)

## Builds on (most cited first, 15 of 15)

- [Dynamic Edge-Conditioned Filters in Convolutional Neural Networks on Graphs](https://mlsanity.com/paper/1704.02901/) (2017)
- [Solving Mixed Integer Programs Using Neural Networks](https://mlsanity.com/paper/2012.13349/) (2020)
- [Reinforcement Learning for Integer Programming: Learning to Cut](https://mlsanity.com/paper/1906.04859/) (2019)
- [Efficient representation and approximation of model predictive control laws via deep learning](https://mlsanity.com/paper/1806.10644/) (2018)
- [Learning to Solve Large-Scale Security-Constrained Unit Commitment Problems](https://mlsanity.com/paper/1902.01697/) (2019)
- [Warm Start of Mixed-Integer Programs for Model Predictive Control of Hybrid Systems](https://mlsanity.com/paper/1910.08251/) (2019)
- [Benders Cut Classification via Support Vector Machines for Solving Two-stage Stochastic Programs](https://mlsanity.com/paper/1906.05994/) (2019)
- [Computationally efficient solution of mixed integer model predictive control problems via machine learning aided Benders Decomposition](https://mlsanity.com/paper/2309.16508/) (2023)
- [A Simple Effective Heuristic for Embedded Mixed-Integer Quadratic Programming](https://mlsanity.com/paper/1509.08416/) (2015)
- [Accelerating Generalized Benders Decomposition for Wireless Resource Allocation](https://mlsanity.com/paper/2003.01294/) (2020)
- [Taking the human out of decomposition-based optimization via artificial intelligence: Part II. Learning to initialize](https://mlsanity.com/paper/2310.07082/) (2023)
- [Accelerating process control and optimization via machine learning: A review](https://mlsanity.com/paper/2412.18529/) (2024)
- [Learning to control inexact Benders decomposition via reinforcement learning](https://mlsanity.com/paper/2508.06700/) (2025)
- [Discovering interpretable piecewise nonlinear model predictive control laws via symbolic decision trees](https://mlsanity.com/paper/2510.10411/) (2025)
- [Graph-Based Imitation and Reinforcement Learning for Efficient Benders Decomposition](https://mlsanity.com/paper/2511.11870/) (2025)

## Abstract (arXiv)

Mixed-integer optimization problems arise in a wide range of control applications. Benders decomposition is a widely used algorithm for solving such problems by decomposing them into a mixed-integer master problem and a continuous subproblem. A key computational bottleneck is the repeated solution of increasingly complex master problems across iterations. In this paper, we propose a feasibility-aware imitation learning framework that predicts the values of the integer variables of the master problem at each iteration while accounting for feasibility with respect to constraints governing admissible integer assignments and the accumulated Benders feasibility cuts. The agent is trained using a two-stage procedure that combines behavioral cloning with a feasibility-based logit adjustment to bias predictions toward assignments that satisfy the evolving cut set. The agent is deployed within an agent-based Benders decomposition framework that combines explicit feasibility checks with a time-limited solver computation of a valid lower bound. The proposed approach retains finite convergence properties, as the lower bound is certified at each iteration. Application to a prototypical case study shows that the proposed method improves solution time relative to existing imitation learning approaches for accelerating Benders decomposition, while preserving solution accuracy.