# Learning to control inexact Benders decomposition via reinforcement learning

arXiv: https://arxiv.org/abs/2508.06700 · HTML: https://mlsanity.com/paper/2508.06700/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- Placed in RL for games and combinatorial optimization, one of 15 directions in Deep reinforcement learning methods.
- Builds on 15 of its 73 references that are in the map.
- First posted on arXiv 8 Aug 2025.

## Placed in

- Deep reinforcement learning methods / [RL for games and combinatorial optimization](https://mlsanity.com/deeprl/rl-for-games-and-combinatorial-optimization/)

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

- [Trust Region Policy Optimization](https://mlsanity.com/paper/1502.05477/) (2015)
- [Machine Learning for Combinatorial Optimization: a Methodological Tour d'Horizon](https://mlsanity.com/paper/1811.06128/) (2018)
- [Reinforcement Learning for Integer Programming: Learning to Cut](https://mlsanity.com/paper/1906.04859/) (2019)
- [Learning Cut Selection for Mixed-Integer Linear Programming via Hierarchical Sequence Model](https://mlsanity.com/paper/2302.00244/) (2023)
- [Automated Dynamic Algorithm Configuration](https://mlsanity.com/paper/2205.13881/) (2022)
- [A Deep Reinforcement Learning Framework For Column Generation](https://mlsanity.com/paper/2206.02568/) (2022)
- [Deep reinforcement learning for process design: Review and perspective](https://mlsanity.com/paper/2308.07822/) (2023)
- [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)
- [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)
- [A Reinforcement-Learning-Based Multiple-Column Selection Strategy for Column Generation](https://mlsanity.com/paper/2312.14213/) (2023)
- [Stochastic Planning and Scheduling with Logic-Based Benders Decomposition](https://mlsanity.com/paper/2012.14074/) (2020)
- [An inexact column-and-constraint generation method to solve two-stage robust optimization problems](https://mlsanity.com/paper/2207.03291/) (2022)
- [Support Vector Machines with the Hard-Margin Loss: Optimal Training via Combinatorial Benders' Cuts](https://mlsanity.com/paper/2207.07690/) (2022)

## Built on by (most cited first, 5 of 5)

- [Graph-Based Imitation and Reinforcement Learning for Efficient Benders Decomposition](https://mlsanity.com/paper/2511.11870/) (2025)
- [Reinforcement learning meets bioprocess control through behaviour cloning: Real-world deployment in an industrial photobioreactor](https://mlsanity.com/paper/2509.06853/) (2025)
- [Learning to Cut: Reinforcement Learning for Benders Decomposition](https://mlsanity.com/paper/2605.06516/) (2026)
- [Feasibility-Aware Imitation Learning for Benders Decomposition](https://mlsanity.com/paper/2604.04801/) (2026)
- [Atoms to Processes: The Role of Artificial Intelligence and Machine Learning in Chemical Engineering](https://mlsanity.com/paper/2610.02014/) (2026)

## Abstract (arXiv)

Benders decomposition (BD), along with its generalized version (GBD), is a widely used algorithm for solving large-scale mixed-integer optimization problems that arise in the operation of process systems. However, the off-the-shelf application to online settings can be computationally inefficient due to the repeated solution of the master problem. An approach to reduce the solution time is to solve the master problem to local optimality. However, identifying the level of suboptimality at each iteration that minimizes the total solution time is nontrivial. In this paper, we propose the application of reinforcement learning to determine the best optimality gap at each GBD iteration. First, we show that the inexact GBD can converge to the optimal solution given a properly designed optimality gap schedule. Next, leveraging reinforcement learning, we learn a policy that minimizes the total solution time, balancing the solution time per iteration with optimality gap improvement. In the resulting RL-iGBD algorithm, the policy adapts the optimality gap at each iteration based on the features of the problem and the solution progress. In numerical experiments on a mixed-integer economic model predictive control problem, we show that the proposed RL-enhanced iGBD method achieves substantial reductions in solution time.