Graph‐based imitation and reinforcement learning for efficient Benders decomposition

Abstract This work introduces an end‐to‐end graph‐based agent for accelerating the computational efficiency of Benders Decomposition. The agent's policy is parameterized by a graph neural network, which takes as input a bipartite graph representation of the master problem and proposes a candidate solution. The agent is trained using a two‐stage approach that combines imitation learning (IL) and reinforcement learning (RL). IL is used to mimic a solver and obtain a warm‐start policy, which is then finetuned using RL with a reward signal that balances feasibility and computational efficiency. We augment the agent with a verification mechanism that checks the agent's prediction for feasibility and solution quality. The framework is evaluated in two case studies: (i) an illustrative mixed‐integer nonlinear program, where it reduces the solution time by 42% without loss of solution quality, and (ii) a closed‐loop irrigation scheduling problem, where it achieves a 23% time reduction without compromising water use efficiency.