Learning to compile relaxed decision diagrams by optimizing the bound

Relaxed decision diagrams certify lower bounds for discrete optimization by merging states under a per-layer width cap. Bound quality depends on which states remain separate, a decision made by hand-designed ranking rules. We study learning this ranking for the traveling salesman problem with a drone. The natural approach ranks states by accumulated cost plus a learned cost-to-go fitted to backward values from a wider relaxed diagram. We show these targets are systematically biased: a relaxed node inherits the most optimistic completion of every state it represents, so its value reflects how much merging occurred rather than the quality of the state, and more data does not remove the bias. Exact targets do not close the gap either: the same policy trained directly on the bound beats exact-target imitation by $1.88$ points at the size where exact targets are computable and by $3.27$ at a larger one, on $88$ and $99$ of $100$ held-out instances. We therefore discard targets and optimize a $22$-parameter ranking policy against the bound compilation produces, which needs no solved instances and preserves validity for every policy. Averaged over optimizer seeds, it improves over imitation by $4.4$–$5.8$ gap points and over the hand-designed $f+h$ rule it corrects by $6.1$–$8.8$, on at least $99$ of $100$ test instances in every configuration from $15$ to $25$ customers, and by $11.8$–$15.7$ over root distance; it reaches in one compilation what a model-free self-guided baseline needs about three times the arc cost to match. Frozen and applied to an independently defined distribution, it is not overtaken by root distance at five times its compilation budget in three of four configurations.