Drift-Conditioned Value of Information for Costly Multi-Label Streams with Delayed Labels

Cost-aware prediction in a multi-label stream must decide which measurement to purchase before delayed labels reveal which risks have changed. Aggregate stream state is insufficient when drift is label local and candidate features have label-specific utility. We formulate drift-conditioned value of information: a delayed residual process estimates a label-local drift posterior, and each feature is scored by its expected reduction in class-balanced decision risk per unit cost, weighted by that posterior. The resulting policy reallocates budget when and where drift aligns with feature-specific risk reduction. On the chronological MultiEURLEX stream, DRIFTBUDGET achieves 70.4 macro-F1 and 58.0 tail recall at 44.5 normalized cost, compared with 66.1, 50.2, and 46.5 for DiFA, while reducing recovery from 17.9 to 10.8 steps. Posterior, global-state, delayed-credit, and delay controls at comparable cost support label-local drift conditioning as the mechanism behind the changed acquisition policy.