We develop novel methodology for active feature acquisition (AFA), the study of sequentially acquiring a dynamic subset of features that minimizes acquisition costs whilst still yielding accurate inference. The AFA framework can be useful in a myriad of domains, including health care applications where the cost of acquiring additional features for a patient (in terms of time, money, risk, etc.) can be weighed against the expected improvement to diagnostic performance. Previous approaches for AFA have employed either: deep learning RL techniques, which have difficulty training policies due to a complicated state and action space; deep learning surrogate generative models, which require modeling complicated multidimensional conditional distributions; or greedy policies, which cannot account for jointly informative feature acquisitions. We show that we can bypass many of these challenges with a novel, nonparametric oracle based approach, which we coin the acquisition conditioned oracle (ACO). Extensive experiments show the superiority of the ACO to state-of-the-art AFA methods when acquiring features for both predictions and general decision-making.