NOCTA: Non-Greedy 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 NOCTA, a Non-Greedy Objective Cost-Tradeoff Acquisition framework that sequentially acquires the most informative features at inference time while accounting for both temporal dynamics and acquisition cost. NOCTA is driven by a novel objective, NOCT, which evaluates a candidate set of future feature-time acquisitions by its expected predictive loss together with its acquisition cost. Since NOCT depends on unobserved future trajectories at inference time, we develop two complementary estimators: (i) NOCT-Contrastive, which learns an embedding of partial observations utilizing the induced distribution over future acquisitions, and (ii) NOCT-Amortized, which directly predicts NOCT for candidate plans with a neural network. Experiments on synthetic and real-world medical datasets demonstrate that both NOCTA estimators outperform existing baselines, achieving higher accuracy at lower acquisition costs.