Conditional Set Decoder for Learning-Augmented Column-and-Constraint Generation

Column-and-constraint generation (C&CG) solves two-stage robust optimization (2RO) problems with a nested min–max–min structure by decomposing the problem and iteratively generating worst-case scenarios through a max–min adversarial problem (AP). Learning-augmented C&CG replaces the AP with a neural network that identifies an adversarial scenario for the current first-stage decision. This prediction depends jointly on the first-stage decision and uncertainty realization. Because the two inputs have different roles and feature descriptions, existing methods encode and aggregate them separately before passing the resulting representations to the prediction network. However, separate aggregation makes their componentwise correspondence implicit, so the network must learn both adversarial-scenario identification and correspondence recovery, which increases the difficulty of the learning task. To address this issue, we propose the Conditional Set Decoder (CSD), which conditions each uncertainty-component representation on its corresponding first-stage decision component before aggregation. CSD preserves their componentwise correspondence before low-dimensional compression and avoids reconstructing it afterward. The architecture remains invariant to joint permutations of corresponding elements, supports value learning, and admits a mixed-integer linear representation. Our analysis shows that, for functions defined by interactions between corresponding elements, conditional aggregation requires a lower representation dimension than separate aggregation. Across three 2RO benchmarks—capital budgeting, robust assignment, and facility location with disruptions—CSD reduces the benchmark-specific median evaluation gap by 52.3%, 62.9%, and nearly 100%, respectively. In a controlled scenario-ranking experiment for facility location with disruptions, CSD recovers 91.1% of decision-conditioned ranking reversals, compared with 0.1% for separate aggregation.