CONSTRAINER: Promptable Graph-Structured Optimization via Constraint Conditioning

Neural methods for graph-structured optimization have achieved strong performance within individual problem classes, but are typically trained for fixed formulations, limiting reuse across related problem variants. Recent progress in foundation models has motivated shared neural backbones trained across multiple graph-structured optimization tasks; however, existing approaches primarily share instance-level representations while treating feasibility constraints implicitly. A key source of shared structure across constrained optimization problems is the constraint set itself, which often exhibits substantial overlap across tasks. We propose CONSTRAINER, a constraint-conditioned framework for graph-structured optimization that treats constraints as structured inputs. Constraint specifications are parsed into operator graphs and encoded using a graph neural network to produce invariant constraint embeddings, which condition a shared backbone model for solution prediction. We evaluate our approach on power grid optimization and mixed-integer linear programming problems, where it shows improved solution optimality and enables efficient transfer learning and generalization compared to baseline methods.