Inverse Mixed-Integer Programming: Learning Constraints then Objective Functions
The paper addresses inverse optimization for mixed-integer linear programs (MILPs) by proposing a two-stage learning approach. It first learns constraints using constraint templates to create an upper bound parameter set ($\phi_{sup}$). Second, it learns the objective weights ($\theta$) by minimizing a suboptimality loss. This method achieves exact reproduction of observed optimal solutions under certain conditions and provides theoretical guarantees on generalization error.