Contrastive Nonmyopic Objective Cost-Tradeoff Acquisition for Longitudinal Data

In many critical domains, features are not freely available at inference time: each measurement may come with a cost of time, money, and risk. Longitudinal prediction further complicates this setting because both features and labels evolve over time, and missing measurements at earlier timepoints may become permanently unavailable. We propose CAPE (Contrastive Acquisition-Plan Embeddings), a partitioning acquisition policy for longitudinal active feature acquisition. CAPE first defines NOCT, an oracle-based objective that scores a set of future feature-time acquisitions by its expected predictive loss together with its acquisition cost. Based on NOCT, CAPE learns a contrastive acquisition-utility manifold of masked partial observations, where proximity reflects the expected utility of future acquisitions. Offline, training states are embedded and partitioned at each rollout timepoint; candidate future plans are scored within each partition using plug-in NOCT, and the best partition-level acquisition plans are cached. During inference, CAPE retrieves the cached plan via nearest-centroid lookup, enabling low-latency adaptive acquisitions. Experiments on synthetic and real-world healthcare datasets demonstrate that CAPE outperforms nonparametric, greedy, and RL-based alternatives, achieving higher accuracy at lower acquisition costs.