  Classification with Costly Features (CwCF) is a classification problem that
includes the cost of features in the optimization criteria. Individually for
each sample, its features are sequentially acquired to maximize accuracy while
minimizing the acquired features' cost. However, existing approaches can only
process data that can be expressed as vectors of fixed length. In real life,
the data often possesses rich and complex structure, which can be more
precisely described with formats such as XML or JSON. The data is hierarchical
and often contains nested lists of objects. In this work, we extend an existing
deep reinforcement learning-based algorithm with hierarchical deep sets and
hierarchical softmax, so that it can directly process this data. The extended
method has greater control over which features it can acquire and, in
experiments with seven datasets, we show that this leads to superior
performance. To showcase the real usage of the new method, we apply it to a
real-life problem of classifying malicious web domains, using an online
service.
