mlsanityData to 14 Oct 2026

Learning to control inexact Benders decomposition via reinforcement learning

arXiv 2508.06700 ↗First posted 8 Aug 2025math.OCcited by 5

On the map: Deep reinforcement learning methods → RL for games and combinatorial optimization

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.

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.

Builds on

15 of 73 references.

References · 15

  1. 2015Trust Region Policy Optimizationcited by 2,580
  2. 2018Machine Learning for Combinatorial Optimization: a Methodological Tour d'Horizoncited by 623
  3. 2019Reinforcement Learning for Integer Programming: Learning to Cutcited by 111
  4. 2023Learning Cut Selection for Mixed-Integer Linear Programming via Hierarchical Sequence Modelcited by 45
  5. 2022Automated Dynamic Algorithm Configurationcited by 39
  6. 2022A Deep Reinforcement Learning Framework For Column Generationcited by 22
  7. 2023Deep reinforcement learning for process design: Review and perspectivecited by 10
  8. 2019Benders Cut Classification via Support Vector Machines for Solving Two-stage Stochastic Programscited by 9
  9. 2023Computationally efficient solution of mixed integer model predictive control problems via machine learning aided Benders Decompositioncited by 6
  10. 2023Taking the human out of decomposition-based optimization via artificial intelligence: Part II. Learning to initializecited by 5
  11. 2024Accelerating process control and optimization via machine learning: A reviewcited by 5
  12. 2023A Reinforcement-Learning-Based Multiple-Column Selection Strategy for Column Generationcited by 4
3 more
  1. 2020Stochastic Planning and Scheduling with Logic-Based Benders Decompositioncited by 2
  2. 2022An inexact column-and-constraint generation method to solve two-stage robust optimization problemscited by 2
  3. 2022Support Vector Machines with the Hard-Margin Loss: Optimal Training via Combinatorial Benders' Cutscited by 2

Built on by

Cited by year (2026 to 14 Oct)

Citing papers per year: 2025: 2; 2026: 3.

5 papers.

  1. 2025Graph-Based Imitation and Reinforcement Learning for Efficient Benders Decompositioncited by 2
  2. 2025Reinforcement learning meets bioprocess control through behaviour cloning: Real-world deployment in an industrial photobioreactorcited by 1
  3. 2026Learning to Cut: Reinforcement Learning for Benders Decompositioncited by 1
  4. 2026Feasibility-Aware Imitation Learning for Benders Decompositioncited by 0
  5. 2026Atoms to Processes: The Role of Artificial Intelligence and Machine Learning in Chemical Engineeringcited by 0

Similar, not cited

Close in wording, no citation either way

  1. 2026A Hybrid Reinforcement and Self-Supervised Learning Aided Benders Decomposition Algorithm
  2. 2022Branch Ranking for Efficient Mixed-Integer Programming via Offline Ranking-based Policy Learning
  3. 2025Beyond Local Selection: Global Cut Selection for Enhanced Mixed-Integer Programming
  4. 2025Machine Learning Algorithms for Improving Exact Classical Solvers in Mixed Integer Continuous Optimization
  5. 2025Planning in Branch-and-Bound: Model-Based Reinforcement Learning for Exact Combinatorial Optimization
  6. 2023Reinforcement Learning with General Utilities: Simpler Variance Reduction and Large State-Action Space
  7. 2026SNAPO: Smooth Neural Adjoint Policy Optimization for Optimal Control via Differentiable Simulation
  8. 2025Learning Branching Policies for MILPs with Proximal Policy Optimization