Solver-Label-Free Pretraining for In-Context Primal Solution Prediction in ILPs

Integer linear programs (ILPs) are a foundational tool for modeling discrete decision-making problems, but solving large-scale ILPs remains computationally challenging due to their NP-hardness. This has motivated machine learning (ML) methods that predict the values of the variables in high-quality solutions, a task known as $\text{primal solution prediction}$. These predictions then guide an exact solver, which narrows its search to promising regions of the solution space. However, most of these methods are trained on solver-labeled instances, which requires hundreds of solver runs, each taking up to an hour, for every problem class. We propose $\text{PrimalPFN}$, a framework that instead uses in-context learning (ICL), predicting solutions for a new instance from a few solved instances of the same class given as input, without retraining. Following prior-data fitted networks (PFNs), we acquire the ICL capability without any solver labels by pretraining on synthetic tasks, in which instances from standard problem generators are labeled by randomly sampled rules that favor feasible, high-quality assignments. At inference time, an exact solver provides the solutions of the few input instances, so the model predicts the solution that solver would find for the new instance. For each problem class, PrimalPFN requires only two solver-labeled instances rather than hundreds, and shares them across all new instances of that class. Across three ILP problem classes, it finds solutions comparable in quality to those of class-specific supervised predictors on two classes and better ones on the third, with a gap to the best known solutions about 40% smaller. Compared with an unsupervised baseline that likewise requires no solver labels for training, PrimalPFN reduces the gap by 39-79%. Moreover, given the same labeled training instances as the supervised predictors, PrimalPFN attains a lower average gap than them on all three classes.