Policy-Conditioned Joint Learning For Node Selection And Variable Branching In Branch-and-Bound

Modern solvers for mixed-integer linear programs (MILPs) rely on branch-andbound, whose efficiency depends largely on two recurring decisions, namely node selection and variable branching. While machine learning has been applied to both decisions, most existing methods learn them separately and overlook their interdependence. To address this issue, we propose a Policy-Conditioned Joint Learning (PCJL) framework, which learns node selection and variable branching as a coupled pair. PCJL encodes the variable–constraint graph of each instance once at the root and reuses this encoding at every branching decision. PCJL then couples two value networks, a branching network that ranks candidate variables in the context of the selected node and a node network that evaluates each candidate node by the cost measured under the action of this learned branching policy. Node targets are thus conditioned on the branching actions taken at deployment and measured under a common reference continuation. To adapt the depth of each descent to the state of the search, PCJL further overrides the fixed plunging rule whenever a gradient-boosted regressor predicts a cheaper depth. Experiments on four NP-hard benchmark families show that PCJL is the fastest of the compared methods on every family and reduces the solving time of SCIP by 15% to 63% on three of them. Moreover, its advantage carries over to larger instances on two families, where the reduction remains 28% to 42%.