Learning to Branch In Context: Adaptive Variable Selection for MILP

A branch-and-bound solve produces observations of how individual branching variables affect the search. Pseudocost rules use these observations to update variable-specific estimates, whereas learned branchers usually consume them only through solver-maintained features or a history of states and actions. We study in-context branching (ICB), which exposes observed directional bound gains as an explicit, identity-linked memory. A learned prior and an evidence-weighted estimator predict directional gains; a fixed scoring rule selects the branching variable. The model is trained by strong-branching distillation and uses new observations without updating its parameters. On canonical combinatorial-auction instances, removing memory from the same checkpoint increases the medium-size node aggregate from 1,205 to 3,204, with all runs solved. On a reconstructed class-disjoint MILP-Evolve cohort, context raises the solved fraction from 55.6% to 69.1% and reduces the paired primal–dual integral by approximately 15%. Comparisons with reproduced branching policies are family-dependent: some transfer results are competitive, but reliability pseudocost branching remains stronger overall. The experiments distinguish improvements due to event memory from those retained when the same policy is evaluated without memory.