We extend the framework of Classification with Costly Features (CwCF) that works with samples of fixed dimensions to trees of varying depth and breadth (similar to a JSON/XML file). In this setting, the sample is a tree - sets of sets of features. Individually for each sample, the task is to sequentially select informative features that help the classification. Each feature has a real-valued cost, and the objective is to maximize accuracy while minimizing the total cost. The process is modeled as an MDP where the states represent the acquired features, and the actions select unknown features. We present a specialized neural network architecture trained through deep reinforcement learning that naturally fits the data and directly selects features in the tree. We demonstrate our method in seven datasets and compare it to two baselines.