Forward Shapley Scoring for Non-Myopic Active Feature Acquisition

Active feature acquisition (AFA) requires an agent to choose a budget-limited set of costly features before making a prediction. Greedy conditional-mutual-information (CMI) and value-of-information policies perform well when useful features are individually informative, but fail under joint-only evidence: a query is valuable only because it enables a future evidence set. To address this, we propose Forward-$\Phi$, a model-based non-myopic acquisition scorer that requires a known structural causal model (SCM) or generative AFA model. Forward-$\Phi$ evaluates a candidate query by its Shapley contribution to budget-feasible future action sets in a cooperative game on the expected forward utility. Two variants share the same game: a raw score that keeps both singleton and interaction value, and a residual score that strips the singleton component to isolate joint-only utility on diagnostic probes. On AFABench CUBE-NM, the raw Monte Carlo (MC) Forward Shapley scorer reaches $0.664 \pm 0.024$ accuracy over five MC seeds, well above all reported baselines including the OL-MFRL ($0.235$) and ODIN-MFRL ($0.160$) reinforcement-learning loops trained under the same split and shared pretraining protocol. Controlled SCM and Bayesian-network (BN) probes confirm the predicted mechanism: Forward-$\Phi$ yields substantial gains when target information is jointly carried, and matches Greedy on greedy-aligned controls. The primary contribution is the belief-conditional Forward Shapley state-action score, a credit-assignment signal derived from Shapley axioms for non-myopic AFA under joint-only evidence.