Learning to Control Feasibility–Objective Trade-off for Integer Linear Programs

Solution predictors for integer linear programs (ILP) struggle to balance feasibility against objective quality, and no existing method learns to control this trade-off at inference. We introduce LibrAx, an unsupervised solution predictor that exposes this trade-off as a spectrum controllable at inference: a single forward pass yields the spectrum. Unlike soft-constrained losses, its semi-hard constrained loss keeps the penalty bounded while retaining an exactness guarantee. On the Very Hard tier of Distributional MIPLIB, LibrAx attains a $2.7\times$ lower primal gap than existing solution predictors on average, with 100% feasibility, producing solutions within 1.2 seconds. ILP solvers need $185$–$453\times$ that time to match LibrAx's solution quality on average, widening to $347$–$603\times$ on an unseen, harder tier.