CORL: Reinforcement Learning of MILP Policies Solved via Branch and Bound

Combinatorial sequential decision making problems are typically modeled as mixed integer linear programs (MILPs) and solved via branch and bound (B&B) algorithms. The inherent difficulty of modeling MILPs that accurately represent stochastic real world problems leads to suboptimal performance in the real world. Recently, machine learning methods have been applied to build MILP models for decision quality rather than how accurately they model the real world problem. However, these approaches typically rely on supervised learning, assume access to true optimal decisions, and use surrogates for the MILP gradients. In this work, we introduce a proof of concept CORL framework that end to end fine tunes an MILP scheme using reinforcement learning (RL) on real world data to maximize its operational performance. We enable this by casting an MILP solved by B&B as a differentiable stochastic policy compatible with RL. We validate the CORL method in a simple illustrative combinatorial sequential decision making example.